[{"data":1,"prerenderedAt":961},["ShallowReactive",2],{"questions:hcf-and-lcm":3},{"bank":4,"contentHash":953,"dependencyHashes":954,"releaseId":960},{"schemaVersion":5,"conceptId":6,"revision":5,"title":7,"intro":8,"sections":9,"questions":42,"sourceIds":944,"reviewStatus":949,"authoring":950},1,"hcf-and-lcm","HCF and LCM question bank","Practise every part of the topic, from listing factors to olympiad puzzles. Questions are grouped by skill and graded **foundation**, **core**, **stretch** and **challenge**. Every question has a full worked solution: after answering, read it even if you were right, because it often shows a faster method. Every numerical answer has been checked by computer.",[10,14,18,22,26,30,34,38],{"id":11,"title":12,"description":13},"factors-hcf","Common factors and the HCF","List factors, find common factors and the highest common factor of two or three numbers.",{"id":15,"title":16,"description":17},"multiples-lcm","Common multiples and the LCM","Skip-count multiples, find common multiples and the lowest common multiple.",{"id":19,"title":20,"description":21},"prime-factorisation","Prime factorisation method","Write numbers in index form and use smallest powers for the HCF and highest powers for the LCM.",{"id":23,"title":24,"description":25},"division-methods","Division methods","Long (continued) division for the HCF, the common division ladder for the LCM, and Euclid’s subtraction form.",{"id":27,"title":28,"description":29},"relationship","HCF × LCM relationship","Use HCF × LCM = product of two numbers, co-primes, and the fact that the HCF divides the LCM.",{"id":31,"title":32,"description":33},"hcf-problems","HCF word problems","Tiles, ropes, containers, rows, packing and \"largest number that divides… leaving remainder\" problems.",{"id":35,"title":36,"description":37},"lcm-problems","LCM word problems","Bells, buses, traffic lights, runners, smallest squares and \"smallest number that leaves remainder…\" problems.",{"id":39,"title":40,"description":41},"mixed-reasoning","Mixed and reasoning","Choosing HCF or LCM, fractions, co-primes, counting, and olympiad-style puzzles.",[43,68,80,89,106,117,127,136,155,165,175,184,203,212,222,232,250,258,269,289,307,317,327,336,345,364,372,383,393,403,411,421,430,441,450,468,479,488,497,506,525,533,551,561,572,582,593,602,614,624,635,644,654,665,676,686,695,703,713,721,729,738,747,757,766,776,793,808,820,830,839,857,878,887,896,905,914,924,933],{"id":44,"section":11,"level":45,"prompt":46,"check":47,"hints":63,"solution":65,"skills":66},"hcf-and-lcm.q001","foundation","Which list shows **all** the common factors of **12** and **20**?",{"kind":48,"options":49,"correct":62},"choice",[50,53,56,59],{"id":51,"label":52},"a","1, 2, 4",{"id":54,"label":55},"b","1, 2, 3, 4",{"id":57,"label":58},"c","2, 4",{"id":60,"label":61},"d","1, 4, 12",[51],[64],"List the factors of 12, then of 20.","Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 20: 1, 2, 4, 5, 10, 20. The numbers in both lists are **1, 2, 4**. Remember 1 is always a common factor.",[67],"common factors",{"id":69,"section":11,"level":45,"prompt":70,"check":71,"hints":75,"solution":77,"skills":78},"hcf-and-lcm.q002","Find the HCF of **18** and **27**.",{"kind":72,"answer":73,"tolerance":74},"number",9,0,[76],"List the factors of 18 and find the biggest that also divides 27.","Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 27: 1, 3, 9, 27. Common: 1, 3, 9. The highest is **9**.",[79],"HCF by listing",{"id":81,"section":11,"level":45,"prompt":82,"check":83,"hints":85,"solution":87,"skills":88},"hcf-and-lcm.q003","Find the HCF of **14** and **35**.",{"kind":72,"answer":84,"tolerance":74},7,[86],"Which numbers divide both 14 and 35?","Factors of 14: 1, 2, 7, 14. Factors of 35: 1, 5, 7, 35. Common: 1, 7. HCF = **7**.",[79],{"id":90,"section":11,"level":45,"prompt":91,"check":92,"hints":101,"solution":103,"skills":104},"hcf-and-lcm.q004","True or false: the HCF of **9** and **16** is **1**.",{"kind":48,"options":93,"correct":100},[94,97],{"id":95,"label":96},"t","True",{"id":98,"label":99},"f","False",[95],[102],"Do 9 and 16 share any factor other than 1?","9 = 3 × 3 and 16 = 2 × 2 × 2 × 2 share no prime factor, so their only common factor is 1. HCF(9, 16) = 1: **true**. Such numbers are called co-prime, even though neither is prime.",[105],"co-primes",{"id":107,"section":11,"level":108,"prompt":109,"check":110,"hints":112,"solution":114,"skills":115},"hcf-and-lcm.q005","core","Find the HCF of **48** and **60**.",{"kind":72,"answer":111,"tolerance":74},12,[113],"Try the biggest factors of 48 first: 48, 24, 16, 12, …","48 = 2⁴ × 3 and 60 = 2² × 3 × 5. Common primes with the smaller powers: 2² × 3 = **12**. Check: 48 ÷ 12 = 4, 60 ÷ 12 = 5, and 4 and 5 share nothing, so no bigger common factor exists.",[116],"HCF",{"id":118,"section":11,"level":108,"prompt":119,"check":120,"hints":121,"solution":124,"skills":125},"hcf-and-lcm.q006","Find the HCF of **24**, **36** and **60**.",{"kind":72,"answer":111,"tolerance":74},[122,123],"The HCF must divide all three numbers.","Find HCF(24, 36) first, then compare with 60.","HCF(24, 36) = 12. Then HCF(12, 60) = 12, because 12 divides 60. So HCF(24, 36, 60) = **12**.",[126],"HCF of three numbers",{"id":128,"section":11,"level":108,"prompt":129,"check":130,"hints":132,"solution":134,"skills":135},"hcf-and-lcm.q007","How many common factors do **36** and **54** have?",{"kind":72,"answer":131,"tolerance":74},6,[133],"The common factors are exactly the factors of the HCF.","HCF(36, 54) = 18. The common factors are the factors of 18: 1, 2, 3, 6, 9, 18. That is **6**.",[67,116],{"id":137,"section":11,"level":108,"prompt":138,"check":139,"hints":150,"solution":152,"skills":153},"hcf-and-lcm.q008","Riya says: \"The HCF of 30 and 45 is 5, because 5 is a factor of both.\" What is wrong?",{"kind":48,"options":140,"correct":149},[141,143,145,147],{"id":51,"label":142},"Nothing, she is right",{"id":54,"label":144},"5 is a common factor but not the highest; the HCF is 15",{"id":57,"label":146},"5 is not a factor of 45",{"id":60,"label":148},"The HCF is 90",[54],[151],"Is there a bigger number that divides both?","5 does divide both, but so does 15 (30 = 15 × 2, 45 = 15 × 3). The common factors are 1, 3, 5, 15, so HCF(30, 45) = **15**. Being *a* common factor is not enough; it must be the highest.",[154],"spot the mistake",{"id":156,"section":11,"level":157,"prompt":158,"check":159,"hints":161,"solution":163,"skills":164},"hcf-and-lcm.q009","stretch","The HCF of two numbers is 1 and one of them is **35**. Which is the smallest number greater than 1 that the other one could be?",{"kind":72,"answer":160,"tolerance":74},2,[162],"35 = 5 × 7. The other number must share neither 5 nor 7.","35 = 5 × 7. Test 2: HCF(35, 2) = 1, since 2 shares no factor with 35. So the smallest possible other number greater than 1 is **2**.",[105],{"id":166,"section":15,"level":45,"prompt":167,"check":168,"hints":170,"solution":172,"skills":173},"hcf-and-lcm.q010","Find the LCM of **4** and **10**.",{"kind":72,"answer":169,"tolerance":74},20,[171],"Count in 10s and test each with 4.","Multiples of 10: 10, 20, … 10 ÷ 4 leaves a remainder; 20 ÷ 4 = 5 exactly. So LCM(4, 10) = **20**. (4 × 10 = 40 is a common multiple, but not the lowest.)",[174],"LCM by listing",{"id":176,"section":15,"level":45,"prompt":177,"check":178,"hints":180,"solution":182,"skills":183},"hcf-and-lcm.q011","Find the LCM of **6** and **9**.",{"kind":72,"answer":179,"tolerance":74},18,[181],"Count in 9s: 9, 18, …","Multiples of 9: 9, 18. Is 18 a multiple of 6? Yes, 6 × 3 = 18. LCM(6, 9) = **18**.",[174],{"id":185,"section":15,"level":45,"prompt":186,"check":187,"hints":198,"solution":200,"skills":201},"hcf-and-lcm.q012","Which of these is a **common multiple** of **3** and **8**?",{"kind":48,"options":188,"correct":197},[189,191,193,195],{"id":51,"label":190},"16",{"id":54,"label":192},"18",{"id":57,"label":194},"24",{"id":60,"label":196},"32",[57],[199],"It must be in the 3 times table and the 8 times table.","24 = 3 × 8 is in both tables. 16 and 32 are multiples of 8 but not 3; 18 is a multiple of 3 but not 8. So **24**.",[202],"common multiples",{"id":204,"section":15,"level":45,"prompt":205,"check":206,"hints":208,"solution":210,"skills":211},"hcf-and-lcm.q013","Write down the **third** common multiple of **4** and **6** (the smallest one counts as the first).",{"kind":72,"answer":207,"tolerance":74},36,[209],"Common multiples are the multiples of the LCM.","LCM(4, 6) = 12. The common multiples are 12, 24, 36, … The third is **36**.",[202],{"id":213,"section":15,"level":108,"prompt":214,"check":215,"hints":217,"solution":219,"skills":220},"hcf-and-lcm.q014","Find the LCM of **12**, **15** and **20**.",{"kind":72,"answer":216,"tolerance":74},60,[218],"Count in 20s and test with 12 and 15.","Multiples of 20: 20, 40, 60. 60 ÷ 12 = 5 and 60 ÷ 15 = 4, both exact. LCM = **60**.",[221],"LCM of three numbers",{"id":223,"section":15,"level":108,"prompt":224,"check":225,"hints":227,"solution":229,"skills":230},"hcf-and-lcm.q015","Find the LCM of **14** and **21**.",{"kind":72,"answer":226,"tolerance":74},42,[228],"14 = 2 × 7 and 21 = 3 × 7.","Both contain 7. LCM = 2 × 3 × 7 = **42**. Check: 42 ÷ 14 = 3, 42 ÷ 21 = 2.",[231],"LCM",{"id":233,"section":15,"level":108,"prompt":234,"check":235,"hints":246,"solution":248,"skills":249},"hcf-and-lcm.q016","Which statement about LCM(8, 12) is correct?",{"kind":48,"options":236,"correct":245},[237,239,241,243],{"id":51,"label":238},"It is 96, because 8 × 12 = 96",{"id":54,"label":240},"It is 24",{"id":57,"label":242},"It is 4",{"id":60,"label":244},"It is 20, because 8 + 12 = 20",[54],[247],"List multiples of 12 and test with 8.","Multiples of 12: 12, 24. 24 = 8 × 3. So LCM(8, 12) = **24**. 96 is a common multiple but not the lowest; 4 is the HCF; adding the numbers has no meaning here.",[154],{"id":251,"section":15,"level":157,"prompt":252,"check":253,"hints":254,"solution":256,"skills":257},"hcf-and-lcm.q017","How many common multiples of **6** and **15** are there between **1** and **200**?",{"kind":72,"answer":131,"tolerance":74},[255],"Every common multiple is a multiple of the LCM.","LCM(6, 15) = 30. Multiples of 30 up to 200: 30, 60, 90, 120, 150, 180. That is **6**.",[202],{"id":259,"section":15,"level":157,"prompt":260,"check":261,"hints":263,"solution":266,"skills":267},"hcf-and-lcm.q018","What is the smallest **4-digit** number that is divisible by **12**, **18** and **30**?",{"kind":72,"answer":262,"tolerance":74},1080,[264,265],"Find LCM(12, 18, 30) first.","Then find the first multiple of it that has 4 digits.","LCM(12, 18, 30) = 180. 1,000 ÷ 180 = 5 remainder 100, so 180 × 5 = 900 is too small. The next multiple is 180 × 6 = **1,080**.",[231,268],"multiples",{"id":270,"section":19,"level":45,"prompt":271,"check":272,"hints":283,"solution":286,"skills":287},"hcf-and-lcm.q019","Write **72** as a product of primes in index form (use ^ for powers if you cannot type them, e.g. 20 = 2^2 × 5).",{"kind":273,"accept":274},"text",[275,276,277,278,279,280,281,282],"2³ × 3²","2^3 × 3^2","2^3*3^2","2³×3²","2^3x3^2","3² × 2³","3^2 × 2^3","2^3 x 3^2",[284,285],"Split 72 into 8 × 9.","8 = 2 × 2 × 2 and 9 = 3 × 3.","72 = 8 × 9 = (2 × 2 × 2) × (3 × 3) = **2³ × 3²**. Check: 8 × 9 = 72.",[288],"prime factorisation",{"id":290,"section":19,"level":45,"prompt":291,"check":292,"hints":303,"solution":305,"skills":306},"hcf-and-lcm.q020","Which is the prime factorisation of **60**?",{"kind":48,"options":293,"correct":302},[294,296,298,300],{"id":51,"label":295},"2 × 30",{"id":54,"label":297},"2² × 3 × 5",{"id":57,"label":299},"4 × 3 × 5",{"id":60,"label":301},"1 × 2² × 3 × 5",[54],[304],"Every factor must be prime.","60 = 2 × 2 × 3 × 5 = **2² × 3 × 5**. 30 and 4 are not prime, and 1 is not prime, so it never appears in a prime factorisation.",[288],{"id":308,"section":19,"level":108,"prompt":309,"check":310,"hints":312,"solution":314,"skills":315},"hcf-and-lcm.q021","Given 90 = 2 × 3² × 5 and 150 = 2 × 3 × 5², find **HCF(90, 150)**.",{"kind":72,"answer":311,"tolerance":74},30,[313],"Common primes, smallest powers.","Common primes: 2 (powers 1 and 1), 3 (powers 2 and 1), 5 (powers 1 and 2). Smallest powers: 2, 3, 5. HCF = 2 × 3 × 5 = **30**.",[316],"HCF by primes",{"id":318,"section":19,"level":108,"prompt":319,"check":320,"hints":322,"solution":324,"skills":325},"hcf-and-lcm.q022","Given 90 = 2 × 3² × 5 and 150 = 2 × 3 × 5², find **LCM(90, 150)**.",{"kind":72,"answer":321,"tolerance":74},450,[323],"All primes, highest powers.","Highest powers: 2, 3², 5². LCM = 2 × 9 × 25 = **450**. Check: 450 ÷ 90 = 5 and 450 ÷ 150 = 3.",[326],"LCM by primes",{"id":328,"section":19,"level":108,"prompt":329,"check":330,"hints":331,"solution":334,"skills":335},"hcf-and-lcm.q023","Use prime factorisation to find **HCF(84, 132)**.",{"kind":72,"answer":111,"tolerance":74},[332,333],"84 = 2² × 3 × 7.","Factorise 132.","84 = 2² × 3 × 7 and 132 = 2² × 3 × 11. Common primes: 2² and 3. HCF = 4 × 3 = **12**.",[316],{"id":337,"section":19,"level":108,"prompt":338,"check":339,"hints":341,"solution":343,"skills":344},"hcf-and-lcm.q024","Use prime factorisation to find **LCM(28, 42, 63)**.",{"kind":72,"answer":340,"tolerance":74},252,[342],"28 = 2² × 7, 42 = 2 × 3 × 7, 63 = 3² × 7.","Highest powers: 2² (from 28), 3² (from 63), 7. LCM = 4 × 9 × 7 = **252**.",[221],{"id":346,"section":19,"level":157,"prompt":347,"check":348,"hints":359,"solution":361,"skills":362},"hcf-and-lcm.q025","a = 2⁴ × 3 × 5² and b = 2² × 3³ × 7. Which is **HCF(a, b)**?",{"kind":48,"options":349,"correct":358},[350,352,354,356],{"id":51,"label":351},"2² × 3",{"id":54,"label":353},"2⁴ × 3³",{"id":57,"label":355},"2⁴ × 3³ × 5² × 7",{"id":60,"label":357},"2² × 3 × 5 × 7",[51],[360],"Only primes in both; smaller power of each.","Common primes: 2 and 3. Smaller powers: 2² and 3¹. 5 and 7 are in only one number. HCF = **2² × 3** = 12.",[316,363],"index form",{"id":365,"section":19,"level":157,"prompt":366,"check":367,"hints":368,"solution":370,"skills":371},"hcf-and-lcm.q026","Aarav wrote HCF(36, 48) = 2⁴ × 3² = 144. What is the correct HCF?",{"kind":72,"answer":111,"tolerance":74},[369],"He used the highest powers. Which rule is that for?","36 = 2² × 3² and 48 = 2⁴ × 3. Aarav took the **highest** powers, which gives the LCM (144). For the HCF take the **smallest** powers: 2² × 3 = **12**. A quick check catches the error: 144 is bigger than 36, so it cannot be a factor of 36.",[154],{"id":373,"section":19,"level":374,"prompt":375,"check":376,"hints":377,"solution":380,"skills":381},"hcf-and-lcm.q027","challenge","How many factors does the HCF of **2⁵ × 3² × 7** and **2³ × 3⁴ × 5** have?",{"kind":72,"answer":111,"tolerance":74},[378,379],"First find the HCF in index form.","A number p^a × q^b has (a + 1)(b + 1) factors.","HCF = 2³ × 3² = 72. Number of factors = (3 + 1)(2 + 1) = **12**. These 12 numbers are exactly the common factors of the two original numbers.",[382],"number of factors",{"id":384,"section":23,"level":45,"prompt":385,"check":386,"hints":388,"solution":390,"skills":391},"hcf-and-lcm.q028","In the long division method for HCF(60, 84), the first step is 84 = 60 × 1 + 24. What number do you divide by in the **next** step?",{"kind":72,"answer":387,"tolerance":74},24,[389],"The remainder becomes the new divisor.","The remainder (24) becomes the new divisor and the old divisor (60) the new dividend: 60 = 24 × 2 + 12. Then 24 = 12 × 2 + 0, so HCF(60, 84) = 12. The next divisor is **24**.",[392],"long division method",{"id":394,"section":23,"level":108,"prompt":395,"check":396,"hints":398,"solution":401,"skills":402},"hcf-and-lcm.q029","Use the long division method to find **HCF(867, 255)**.",{"kind":72,"answer":397,"tolerance":74},51,[399,400],"867 = 255 × 3 + 102.","Now divide 255 by 102.","Steps: 867 = 255 × 3 + 102; 255 = 102 × 2 + 51; 102 = 51 × 2 + 0. The last divisor is **51**.",[392],{"id":404,"section":23,"level":108,"prompt":405,"check":406,"hints":407,"solution":409,"skills":410},"hcf-and-lcm.q030","Use the long division method to find **HCF(1,260, 7,344)**.",{"kind":72,"answer":207,"tolerance":74},[408],"Start with 7,344 ÷ 1,260.","Steps: 7,344 = 1,260 × 5 + 1044; 1,260 = 1,044 × 1 + 216; 1,044 = 216 × 4 + 180; 216 = 180 × 1 + 36; 180 = 36 × 5 + 0. HCF = **36**.",[392],{"id":412,"section":23,"level":108,"prompt":413,"check":414,"hints":416,"solution":418,"skills":419},"hcf-and-lcm.q031","Use the common division (ladder) method to find **LCM(16, 24, 36)**.",{"kind":72,"answer":415,"tolerance":74},144,[417],"Divide the row by 2 while at least two numbers are even.","Row 16, 24, 36 → ÷ 2 → 8, 12, 18 → ÷ 2 → 4, 6, 9 → ÷ 2 → 2, 3, 9 → ÷ 3 → 2, 1, 3. No prime now divides two numbers. LCM = 2 × 2 × 2 × 3 × 2 × 1 × 3 = **144**.",[420],"common division method",{"id":422,"section":23,"level":108,"prompt":423,"check":424,"hints":426,"solution":428,"skills":429},"hcf-and-lcm.q032","In the ladder for LCM(12, 18, 30), the divisors on the left are 2 and 3 and the bottom row is 2, 3, 5. What is the LCM?",{"kind":72,"answer":425,"tolerance":74},180,[427],"Multiply the divisors and the bottom row.","LCM = 2 × 3 × 2 × 3 × 5 = **180**.",[420],{"id":431,"section":23,"level":157,"prompt":432,"check":433,"hints":435,"solution":438,"skills":439},"hcf-and-lcm.q033","How many division steps (including the last one with remainder 0) does the long division method take for **HCF(144, 89)**?",{"kind":72,"answer":434,"tolerance":74},10,[436,437],"144 and 89 are neighbouring Fibonacci numbers.","Every quotient will be 1 until the very end.","Steps: 144 = 89 × 1 + 55; 89 = 55 × 1 + 34; 55 = 34 × 1 + 21; 34 = 21 × 1 + 13; 21 = 13 × 1 + 8; 13 = 8 × 1 + 5; 8 = 5 × 1 + 3; 5 = 3 × 1 + 2; 3 = 2 × 1 + 1; 2 = 1 × 2 + 0. That is **10 steps**, and HCF = 1. Neighbouring Fibonacci numbers are the slowest case for Euclid’s method.",[392,440],"Fibonacci",{"id":442,"section":23,"level":157,"prompt":443,"check":444,"hints":445,"solution":447,"skills":448},"hcf-and-lcm.q034","Use the subtraction version of Euclid (keep subtracting the smaller from the larger) to find **HCF(91, 35)**.",{"kind":72,"answer":84,"tolerance":74},[446],"91 − 35 = 56. Now use (56, 35).","(91, 35) → (56, 35) → (35, 21) → (21, 14) → (14, 7) → (7, 7) → HCF = **7**. Each subtraction keeps the same common factors.",[449],"Euclid by subtraction",{"id":451,"section":23,"level":157,"prompt":452,"check":453,"hints":464,"solution":466,"skills":467},"hcf-and-lcm.q035","For HCF(4, 6, 9), a student uses the LCM ladder, gets divisors 2 and 3, and says the HCF is 6. Why is this wrong?",{"kind":48,"options":454,"correct":463},[455,457,459,461],{"id":51,"label":456},"The ladder divisors only divided two of the three numbers each time",{"id":54,"label":458},"The ladder always gives the LCM, so HCF = 36",{"id":57,"label":460},"It is correct",{"id":60,"label":462},"6 is not a factor of 6",[51],[465],"Does 2 divide 9? Does 3 divide 4?","In the ladder, 2 divided only 4 and 6, and 3 divided only 6 and 9. For the HCF a divisor must divide **all** the numbers. No number except 1 divides 4, 6 and 9, so HCF(4, 6, 9) = **1**.",[154],{"id":469,"section":23,"level":374,"prompt":470,"check":471,"hints":473,"solution":476,"skills":477},"hcf-and-lcm.q036","Find the HCF of **1,147**, **1,591** and **2,183** (use long division twice).",{"kind":72,"answer":472,"tolerance":74},37,[474,475],"First find HCF(1,147, 1,591).","Then find the HCF of that answer with 2,183.","HCF(1,591, 1,147): 1,591 = 1,147 × 1 + 444; 1,147 = 444 × 2 + 259; 444 = 259 × 1 + 185; 259 = 185 × 1 + 74; 185 = 74 × 2 + 37; 74 = 37 × 2 + 0 → 37. Then 2,183 = 37 × 59 + 0, so 37 divides 2,183 and the HCF of all three is **37**.",[392,478],"three numbers",{"id":480,"section":27,"level":45,"prompt":481,"check":482,"hints":483,"solution":485,"skills":486},"hcf-and-lcm.q037","The HCF of 8 and 12 is 4. Their product is 96. What is their LCM?",{"kind":72,"answer":387,"tolerance":74},[484],"HCF × LCM = product of the two numbers.","LCM = product ÷ HCF = 96 ÷ 4 = **24**.",[487],"HCF × LCM",{"id":489,"section":27,"level":45,"prompt":490,"check":491,"hints":493,"solution":495,"skills":496},"hcf-and-lcm.q038","Two co-prime numbers are **7** and **9**. What is their LCM?",{"kind":72,"answer":492,"tolerance":74},63,[494],"For co-primes, HCF = 1.","HCF(7, 9) = 1, so LCM = 7 × 9 = **63**.",[105],{"id":498,"section":27,"level":108,"prompt":499,"check":500,"hints":502,"solution":504,"skills":505},"hcf-and-lcm.q039","The HCF of two numbers is **16** and their LCM is **192**. One number is **48**. Find the other.",{"kind":72,"answer":501,"tolerance":74},64,[503],"HCF × LCM = a × b.","16 × 192 = 3072 = 48 × other. Other = 3072 ÷ 48 = **64**. Check: HCF(48, 64) = 16 and LCM(48, 64) = 192.",[487],{"id":507,"section":27,"level":108,"prompt":508,"check":509,"hints":520,"solution":522,"skills":523},"hcf-and-lcm.q040","Can two numbers have HCF **12** and LCM **90**?",{"kind":48,"options":510,"correct":519},[511,513,515,517],{"id":51,"label":512},"Yes, 12 and 90",{"id":54,"label":514},"Yes, 30 and 36",{"id":57,"label":516},"No, because 12 does not divide 90",{"id":60,"label":518},"No, because 90 is not a multiple of 9",[57],[521],"The HCF always divides the LCM.","90 ÷ 12 = 7 remainder 6, so 12 does not divide 90. Since the HCF must divide the LCM, **no such pair exists**. (Check option a: HCF(12, 90) = 6.)",[524],"HCF divides LCM",{"id":526,"section":27,"level":108,"prompt":527,"check":528,"hints":529,"solution":531,"skills":532},"hcf-and-lcm.q041","The product of two numbers is **1,500** and their LCM is **150**. What is their HCF?",{"kind":72,"answer":434,"tolerance":74},[530],"HCF = product ÷ LCM.","1,500 ÷ 150 = **10**. (For example 30 and 50: HCF 10, LCM 150, product 1,500.)",[487],{"id":534,"section":27,"level":108,"prompt":535,"check":536,"hints":547,"solution":549,"skills":550},"hcf-and-lcm.q042","For **4, 6** and **8**, HCF = 2 and LCM = 24. Is HCF × LCM equal to 4 × 6 × 8?",{"kind":48,"options":537,"correct":546},[538,540,542,544],{"id":51,"label":539},"Yes, both are 48",{"id":54,"label":541},"No: 48 ≠ 192",{"id":57,"label":543},"Yes, both are 192",{"id":60,"label":545},"It cannot be checked",[54],[548],"Work out both sides.","HCF × LCM = 2 × 24 = 48, but 4 × 6 × 8 = 192. **Not equal.** The rule HCF × LCM = product works only for two numbers.",[478],{"id":552,"section":27,"level":157,"prompt":553,"check":554,"hints":556,"solution":558,"skills":559},"hcf-and-lcm.q043","Two numbers are in the ratio **3 : 5** and their HCF is **8**. What is their LCM?",{"kind":72,"answer":555,"tolerance":74},120,[557],"Write the numbers as 3 × 8 and 5 × 8.","The numbers are 24 and 40 (3 and 5 are co-prime, so the HCF is exactly 8). LCM = 8 × 3 × 5 = **120**.",[560,487],"ratio",{"id":562,"section":27,"level":157,"prompt":563,"check":564,"hints":566,"solution":569,"skills":570},"hcf-and-lcm.q044","The LCM of two numbers is **14 times** their HCF, and HCF + LCM = **600**. One number is **80**. Find the other.",{"kind":72,"answer":565,"tolerance":74},280,[567,568],"Let HCF = h, so LCM = 14h and h + 14h = 600.","Then use HCF × LCM = product.","15h = 600, so HCF h = 40 and LCM = 560. Product = 40 × 560 = 22,400 = 80 × other, so other = **280**. Check: HCF(80, 280) = 40 and LCM = 560.",[487,571],"algebra",{"id":573,"section":27,"level":374,"prompt":574,"check":575,"hints":577,"solution":579,"skills":580},"hcf-and-lcm.q045","How many pairs of whole numbers (a, b) with a ≤ b have HCF **15** and LCM **1,260**? (Enter 0 if no such pair exists.)",{"kind":72,"answer":576,"tolerance":74},4,[578],"Does 15 divide 1,260?","1,260 ÷ 15 = 84, so 15 does divide 1,260. Write a = 15m, b = 15n with m × n = 84 = 2² × 3 × 7 and HCF(m, n) = 1. Each prime power (4, 3, 7) goes wholly to m or n: 2³ = 8 assignments, i.e. 4 pairs with m ≤ n: (1, 84), (3, 28), (4, 21), (7, 12). Pairs: (15, 1,260), (45, 420), (60, 315), (105, 180). **4 pairs.**",[581],"counting pairs",{"id":583,"section":31,"level":45,"prompt":584,"check":585,"hints":588,"solution":590,"skills":591},"hcf-and-lcm.q046","A florist has **24 roses** and **32 lilies**. She makes identical bunches with no flowers left over. What is the **greatest** number of bunches she can make?",{"kind":72,"answer":586,"tolerance":74,"unit":587},8,"bunches",[589],"The number of bunches must divide 24 and 32.","HCF(24, 32) = 8. So **8 bunches**, each with 3 roses and 4 lilies.",[592],"HCF word problem",{"id":594,"section":31,"level":45,"prompt":595,"check":596,"hints":598,"solution":600,"skills":601},"hcf-and-lcm.q047","Two ropes are **36 m** and **48 m** long. They are cut into pieces of equal length, as long as possible, with nothing wasted. How long is each piece?",{"kind":72,"answer":111,"tolerance":74,"unit":597},"m",[599],"The piece length must divide both lengths.","HCF(36, 48) = 12. Each piece is **12 m**: 3 pieces from the first rope and 4 from the second.",[592],{"id":603,"section":31,"level":108,"prompt":604,"check":605,"hints":608,"solution":611,"skills":612},"hcf-and-lcm.q048","A hall is **15 m 30 cm** long and **9 m 18 cm** wide. What is the side of the **largest** square tile (in cm) that covers the floor exactly?",{"kind":72,"answer":606,"tolerance":74,"unit":607},306,"cm",[609,610],"Convert to centimetres: 1,530 cm and 918 cm.","Find their HCF.","1,530 = 2 × 3² × 5 × 17 and 918 = 2 × 3³ × 17. Common part: 2 × 3² × 17 = **306 cm**. That needs 5 × 3 = 15 tiles.",[592,613],"unit conversion",{"id":615,"section":31,"level":108,"prompt":616,"check":617,"hints":620,"solution":622,"skills":623},"hcf-and-lcm.q049","Three containers hold **420 L**, **588 L** and **756 L** of oil. What is the largest measuring can that measures each exactly?",{"kind":72,"answer":618,"tolerance":74,"unit":619},84,"L",[621],"Find the HCF of all three.","420 = 2² × 3 × 5 × 7, 588 = 2² × 3 × 7², 756 = 2² × 3³ × 7. Common: 2² × 3 × 7 = **84 L**.",[592,478],{"id":625,"section":31,"level":108,"prompt":626,"check":627,"hints":630,"solution":633,"skills":634},"hcf-and-lcm.q050","For a march past, **408 students** of Class 6 and **216 students** of Class 7 must stand in rows of equal size, each row from one class only. What is the **least** number of rows possible?",{"kind":72,"answer":628,"tolerance":74,"unit":629},26,"rows",[631,632],"Fewest rows means the biggest possible row size.","Row size = HCF(408, 216).","Row size = HCF(408, 216) = 24. Rows: 408 ÷ 24 = 17 and 216 ÷ 24 = 9. Least number of rows = **26**.",[592],{"id":636,"section":31,"level":108,"prompt":637,"check":638,"hints":640,"solution":642,"skills":643},"hcf-and-lcm.q051","A kirana shop owner has **96 kg** of rice and **120 kg** of wheat. She packs them in bags that all hold the **same** weight, as heavy as possible, with no mixing. How many bags does she need in all?",{"kind":72,"answer":73,"tolerance":74,"unit":639},"bags",[641],"Bag size = HCF(96, 120).","Bag size = HCF(96, 120) = 24 kg. Rice: 96 ÷ 24 = 4 bags; wheat: 120 ÷ 24 = 5 bags. Total **9 bags**.",[592],{"id":645,"section":31,"level":157,"prompt":646,"check":647,"hints":649,"solution":651,"skills":652},"hcf-and-lcm.q052","What is the **largest** number that divides **245** and **1,029** leaving remainder **5** in each case?",{"kind":72,"answer":648,"tolerance":74},16,[650],"Subtract the remainder from each number first.","The number must divide 245 − 5 = 240 and 1,029 − 5 = 1,024 exactly. HCF(240, 1,024) = **16**. It is bigger than 5, so remainder 5 is possible. Check: 245 = 16 × 15 + 5 ✓, 1,029 = 16 × 64 + 5 ✓.",[653],"remainder problem",{"id":655,"section":31,"level":157,"prompt":656,"check":657,"hints":659,"solution":662,"skills":663},"hcf-and-lcm.q053","Find the largest number that divides **62**, **132** and **237** leaving the **same** remainder in each case.",{"kind":72,"answer":658,"tolerance":74},35,[660,661],"If a and b leave the same remainder when divided by d, then d divides b − a.","Take the HCF of the differences.","Differences: 132 − 62 = 70 and 237 − 132 = 105. The number must divide both: HCF(70, 105) = **35**. Check: 62 = 35 × 1 + 27, 132 = 35 × 3 + 27, 237 = 35 × 6 + 27. Same remainder 27. ✓",[653,664],"reasoning",{"id":666,"section":31,"level":374,"prompt":667,"check":668,"hints":670,"solution":673,"skills":674},"hcf-and-lcm.q054","A rectangular garden **1,125 cm** by **1,575 cm** is to be paved with identical square tiles, as large as possible. How many tiles are needed?",{"kind":72,"answer":658,"tolerance":74,"unit":669},"tiles",[671,672],"Tile side = HCF(1,125, 1,575).","Count tiles along each side and multiply.","HCF(1,125, 1,575) = 225 cm. Along one side: 1,125 ÷ 225 = 5; along the other: 1,575 ÷ 225 = 7. Tiles = 5 × 7 = **35**.",[592,675],"area",{"id":677,"section":35,"level":45,"prompt":678,"check":679,"hints":681,"solution":683,"skills":684},"hcf-and-lcm.q055","Two bells ring every **8 minutes** and **12 minutes**. They ring together at 10:00. After how many minutes do they next ring together?",{"kind":72,"answer":387,"tolerance":74,"unit":680},"minutes",[682],"Find the first common multiple of 8 and 12.","Multiples of 12: 12, 24. 24 = 8 × 3. So LCM = **24 minutes**: they ring together again at 10:24.",[685],"LCM word problem",{"id":687,"section":35,"level":45,"prompt":688,"check":689,"hints":691,"solution":693,"skills":694},"hcf-and-lcm.q056","Sweets are to be shared equally among either **5** or **6** children with none left over. What is the **least** number of sweets needed?",{"kind":72,"answer":311,"tolerance":74,"unit":690},"sweets",[692],"The number must be divisible by 5 and by 6.","LCM(5, 6) = **30** (5 and 6 are co-prime, so it is 5 × 6).",[685],{"id":696,"section":35,"level":45,"prompt":697,"check":698,"hints":699,"solution":701,"skills":702},"hcf-and-lcm.q057","Buses to Mysuru leave every **20 minutes** and to Ooty every **30 minutes**. Both leave at 6:00 a.m. How many minutes later do they next leave together?",{"kind":72,"answer":216,"tolerance":74,"unit":680},[700],"LCM of 20 and 30.","LCM(20, 30) = **60 minutes**, so at 7:00 a.m.",[685],{"id":704,"section":35,"level":108,"prompt":705,"check":706,"hints":709,"solution":711,"skills":712},"hcf-and-lcm.q058","Three traffic lights change every **48 s**, **72 s** and **108 s**. They change together at 7:00:00 a.m. After how many **seconds** do they next change together?",{"kind":72,"answer":707,"tolerance":74,"unit":708},432,"s",[710],"48 = 2⁴ × 3, 72 = 2³ × 3², 108 = 2² × 3³.","LCM = 2⁴ × 3³ = **432 s**, which is 7 minutes 12 seconds, so at 7:07:12 a.m.",[685,478],{"id":714,"section":35,"level":108,"prompt":715,"check":716,"hints":717,"solution":719,"skills":720},"hcf-and-lcm.q059","On a circular track, Sneha takes **18 minutes** per round and Ishaan **12 minutes**. They start together at the same point in the same direction. After how many minutes do they next meet at the starting point?",{"kind":72,"answer":207,"tolerance":74,"unit":680},[718],"LCM of the lap times.","LCM(18, 12) = **36 minutes**. Sneha has run 2 rounds and Ishaan 3.",[685],{"id":722,"section":35,"level":108,"prompt":723,"check":724,"hints":725,"solution":727,"skills":728},"hcf-and-lcm.q060","What is the side of the **smallest** square (in cm) that can be made by placing **15 cm × 20 cm** tiles side by side, all the same way round?",{"kind":72,"answer":216,"tolerance":74,"unit":607},[726],"The square side must be a multiple of both 15 and 20.","LCM(15, 20) = **60 cm**. It uses (60 ÷ 15) × (60 ÷ 20) = 4 × 3 = 12 tiles.",[685,675],{"id":730,"section":35,"level":108,"prompt":731,"check":732,"hints":734,"solution":736,"skills":737},"hcf-and-lcm.q061","Find the smallest number which leaves remainder **3** when divided by **8**, **12** and **18** (other than 3 itself).",{"kind":72,"answer":733,"tolerance":74},75,[735],"Subtract 3: the result is a common multiple of 8, 12 and 18.","LCM(8, 12, 18) = 72. The number is 72 + 3 = **75**. Check: 75 = 8 × 9 + 3 = 12 × 6 + 3 = 18 × 4 + 3.",[653],{"id":739,"section":35,"level":157,"prompt":740,"check":741,"hints":743,"solution":745,"skills":746},"hcf-and-lcm.q062","Find the smallest number which, when **increased by 7**, is divisible by **16, 24** and **36**.",{"kind":72,"answer":742,"tolerance":74},137,[744],"Number + 7 must be a common multiple.","LCM(16, 24, 36) = 144. Number + 7 = 144, so the number is **137**.",[653],{"id":748,"section":35,"level":157,"prompt":749,"check":750,"hints":752,"solution":755,"skills":756},"hcf-and-lcm.q063","Find the smallest number that leaves remainders **4, 5** and **6** when divided by **5, 6** and **7** respectively.",{"kind":72,"answer":751,"tolerance":74},209,[753,754],"Each remainder is 1 less than its divisor.","So the number + 1 is divisible by 5, 6 and 7.","Number + 1 is a common multiple of 5, 6, 7. LCM = 210, so the number is **209**. Check: 209 = 5 × 41 + 4 = 6 × 34 + 5 = 7 × 29 + 6.",[653],{"id":758,"section":35,"level":157,"prompt":759,"check":760,"hints":762,"solution":764,"skills":765},"hcf-and-lcm.q064","What is the **greatest 4-digit** number exactly divisible by **15, 24** and **36**?",{"kind":72,"answer":761,"tolerance":74},9720,[763],"Find the LCM, then the largest multiple below 10,000.","LCM(15, 24, 36) = 360. 9,999 ÷ 360 = 27 remainder 279, so the answer is 360 × 27 = **9,720**.",[231,268],{"id":767,"section":35,"level":374,"prompt":768,"check":769,"hints":771,"solution":774,"skills":775},"hcf-and-lcm.q065","Three runners run laps of a track in **60 s**, **72 s** and **90 s**. They start together. How many laps has the **fastest** runner completed when all three are next together at the start?",{"kind":72,"answer":131,"tolerance":74,"unit":770},"laps",[772,773],"Find the LCM of the lap times.","Divide by the fastest lap time.","LCM(60, 72, 90) = 360 s (6 minutes). The fastest runner (60 s) has done 360 ÷ 60 = **6 laps**; the others 5 and 4.",[685],{"id":777,"section":39,"level":45,"prompt":778,"check":779,"hints":788,"solution":790,"skills":791},"hcf-and-lcm.q066","\"What is the biggest box size that can pack 18 pencils and 30 pens without mixing or leftovers?\" This needs the…",{"kind":48,"options":780,"correct":787},[781,782,783,785],{"id":51,"label":116},{"id":54,"label":231},{"id":57,"label":784},"product",{"id":60,"label":786},"sum",[51],[789],"Are you splitting things up, or waiting for things to meet?","You are splitting 18 and 30 into equal groups, as big as possible: **HCF**. HCF(18, 30) = 6.",[792],"HCF or LCM?",{"id":794,"section":39,"level":45,"prompt":795,"check":796,"hints":804,"solution":806,"skills":807},"hcf-and-lcm.q067","\"Two lighthouses flash every 9 s and 15 s. When do they flash together?\" This needs the…",{"kind":48,"options":797,"correct":803},[798,799,800,802],{"id":51,"label":116},{"id":54,"label":231},{"id":57,"label":801},"difference",{"id":60,"label":784},[54],[805],"Repeating events meeting again.","Repeating flashes meet at a common multiple; the first is the **LCM**: LCM(9, 15) = 45 s.",[792],{"id":809,"section":39,"level":108,"prompt":810,"check":811,"hints":815,"solution":817,"skills":818},"hcf-and-lcm.q068","Simplify **144⁄180** to its lowest terms in one step.",{"kind":812,"numerator":576,"denominator":813,"acceptEquivalent":814},"fraction",5,false,[816],"Divide top and bottom by HCF(144, 180).","HCF(144, 180) = 36. 144 ÷ 36 = 4 and 180 ÷ 36 = 5, so **4⁄5**.",[819],"simplifying fractions",{"id":821,"section":39,"level":108,"prompt":822,"check":823,"hints":825,"solution":827,"skills":828},"hcf-and-lcm.q069","Work out **5⁄6 + 4⁄9** using the lowest common denominator. Give the answer as an improper fraction in lowest terms.",{"kind":812,"numerator":824,"denominator":179,"acceptEquivalent":814},23,[826],"LCM(6, 9) = 18.","LCM(6, 9) = 18. 5⁄6 = 15⁄18 and 4⁄9 = 8⁄18. Sum = **23⁄18** (which is 1 5⁄18). HCF(23, 18) = 1, so it is already in lowest terms.",[829],"adding fractions",{"id":831,"section":39,"level":108,"prompt":832,"check":833,"hints":834,"solution":836,"skills":837},"hcf-and-lcm.q070","Work out **7⁄12 − 3⁄8** in lowest terms.",{"kind":812,"numerator":813,"denominator":387,"acceptEquivalent":814},[835],"LCM(12, 8) = 24.","LCM(12, 8) = 24. 7⁄12 = 14⁄24 and 3⁄8 = 9⁄24. Difference = **5⁄24**.",[838],"subtracting fractions",{"id":840,"section":39,"level":108,"prompt":841,"check":842,"hints":853,"solution":855,"skills":856},"hcf-and-lcm.q071","Which statement is **always** true for two whole numbers a and b?",{"kind":48,"options":843,"correct":852},[844,846,848,850],{"id":51,"label":845},"LCM(a, b) = a × b",{"id":54,"label":847},"HCF(a, b) divides LCM(a, b)",{"id":57,"label":849},"HCF(a, b) is prime",{"id":60,"label":851},"LCM(a, b) is even",[54],[854],"Test each statement with 4 and 6.","The HCF divides a, and a divides the LCM, so the HCF divides the LCM: **b**. Counterexamples for the others: LCM(4, 6) = 12 ≠ 24; HCF(12, 24) = 12 is not prime; LCM(3, 5) = 15 is odd.",[664],{"id":858,"section":39,"level":157,"prompt":859,"check":860,"hints":874,"solution":876,"skills":877},"hcf-and-lcm.q072","Which pairs are co-prime? (Choose all that apply.)",{"kind":48,"options":861,"correct":873},[862,864,866,868,870],{"id":51,"label":863},"15 and 28",{"id":54,"label":865},"21 and 35",{"id":57,"label":867},"16 and 27",{"id":60,"label":869},"33 and 44",{"id":871,"label":872},"e","49 and 50",[51,57,871],[875],"Look for a shared prime factor in each pair.","15 = 3 × 5 and 28 = 2² × 7: HCF 1 ✓. 21 and 35 share 7 ✗. 16 = 2⁴ and 27 = 3³: HCF 1 ✓. 33 and 44 share 11 ✗. 49 and 50 are consecutive: HCF 1 ✓. So **a, c and e**.",[105],{"id":879,"section":39,"level":157,"prompt":880,"check":881,"hints":882,"solution":885,"skills":886},"hcf-and-lcm.q073","Two numbers differ by **12**. Their HCF is as large as possible and the smaller number is between 30 and 40. What is the smaller number?",{"kind":72,"answer":207,"tolerance":74},[883,884],"The HCF divides the difference, 12, so it is at most 12.","For HCF 12, both numbers must be multiples of 12.","The HCF divides 12, so the largest possible HCF is 12, which needs both numbers to be multiples of 12 that differ by 12. The only multiple of 12 between 30 and 40 is **36** (pair 36 and 48, HCF 12).",[664,801],{"id":888,"section":39,"level":157,"prompt":889,"check":890,"hints":891,"solution":893,"skills":894},"hcf-and-lcm.q074","How many numbers from **1 to 300** are divisible by **both 8 and 12**?",{"kind":72,"answer":111,"tolerance":74},[892],"Divisible by both means divisible by the LCM.","LCM(8, 12) = 24. 300 ÷ 24 = 12 remainder 12, so **12** numbers. (Using 8 × 12 = 96 would wrongly give 3.)",[895,231],"counting",{"id":897,"section":39,"level":374,"prompt":898,"check":899,"hints":900,"solution":902,"skills":903},"hcf-and-lcm.q075","Two numbers add up to **216** and their HCF is **27**. How many such pairs (a, b) with a smaller than b are there?",{"kind":72,"answer":160,"tolerance":74},[901],"Write a = 27m and b = 27n with m + n = 8 and m, n co-prime.","m + n = 216 ÷ 27 = 8, with m smaller than n and HCF(m, n) = 1: (1, 7) and (3, 5) work; (2, 6) shares 2; (4, 4) is not allowed. Pairs: (27, 189) and (81, 135). **2 pairs.**",[904,116],"olympiad",{"id":906,"section":39,"level":374,"prompt":907,"check":908,"hints":910,"solution":912,"skills":913},"hcf-and-lcm.q076","What is the smallest number that is divisible by **every** whole number from **1 to 12**?",{"kind":72,"answer":909,"tolerance":74},27720,[911],"Take the highest power of each prime up to 12.","Highest prime powers up to 12: 2³ = 8, 3² = 9, 5, 7, 11. LCM = 8 × 9 × 5 × 7 × 11 = **27,720**.",[231,904],{"id":915,"section":39,"level":374,"prompt":916,"check":917,"hints":918,"solution":921,"skills":922},"hcf-and-lcm.q077","Find the smallest positive number that leaves remainder **2** when divided by **3**, remainder **3** when divided by **5**, and remainder **2** when divided by **7**.",{"kind":72,"answer":824,"tolerance":74},[919,920],"List numbers with remainder 2 on division by 7: 2, 9, 16, 23, …","Test each with 3 and 5.","Numbers with remainder 2 on ÷ 7: 2, 9, 16, 23, … 2 ÷ 5 leaves 2 ✗; 9 ÷ 3 leaves 0 ✗; 16 ÷ 3 leaves 1 ✗; 23 ÷ 3 leaves 2 ✓ and 23 ÷ 5 leaves 3 ✓. Answer **23**. This is Sunzi’s ancient puzzle; the next answer is 23 + LCM(3, 5, 7) = 128.",[923,904],"Chinese remainder",{"id":925,"section":39,"level":374,"prompt":926,"check":927,"hints":928,"solution":930,"skills":931},"hcf-and-lcm.q078","A grid of squares is **15 by 24**. How many squares does a straight line from one corner to the opposite corner pass through?",{"kind":72,"answer":207,"tolerance":74},[929],"Use m + n − HCF(m, n).","15 + 24 − HCF(15, 24) = 39 − 3 = **36**. The line passes through 2 inner grid corners, where it enters a new row and column at once.",[904,932],"geometry",{"id":934,"section":39,"level":374,"prompt":935,"check":936,"hints":938,"solution":940,"skills":941},"hcf-and-lcm.q079","With a **9-litre** and a **12-litre** jug (fill, empty, pour between them), what is the **smallest** positive amount of water you can measure exactly?",{"kind":72,"answer":937,"tolerance":74,"unit":619},3,[939],"Every amount you can make is a multiple of the HCF.","All reachable amounts are multiples of HCF(9, 12) = 3, and 3 itself is possible: fill the 12 L jug, pour into the 9 L jug, and **3 litres** remain.",[942,943],"Bezout","puzzle",[945,946,947,948],"hcf-and-lcm-ncert-class6-playing-with-numbers","hcf-and-lcm-ncert-class10-real-numbers","hcf-and-lcm-mathsisfun-gcf","hcf-and-lcm-mathsisfun-lcm","needs_review",{"generatedBy":951,"notes":952},"claude-code","Draft; every numeric answer computed and asserted in Python (math.gcd \u002F lcm). Pending owner review.","67e9793baa58aed9d2d38890ebf70257dd9957d8b4a719a84480a61d0f347f9f",{"logic:questions":955,"source:hcf-and-lcm-mathsisfun-gcf":956,"source:hcf-and-lcm-mathsisfun-lcm":957,"source:hcf-and-lcm-ncert-class10-real-numbers":958,"source:hcf-and-lcm-ncert-class6-playing-with-numbers":959},"e7fd7c240a65bea1bff6277f7af7cca65e2c7fcb13c6d756cb943d53f3cbc948","8499aa4d85d927e518cacd55fa1f7870d1da1332351d07b641c2a1cc6c885659","722e7f7db3c09e9e29bf5c0f363173f52eb56ef08d1bd84ad3f51890d1375d07","48d1fd4c018916e9edeb2f76b15a8eb3cb83c72b08a9d3ab332a3c167fe9be0b","82c5fcc908046567f1a1bdb191f9b28fd42600389720d981bc1965d0c1542772","preview-7e1cbbcc4f",1789899599831]