HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 418 · 40 questions

How to solve it (Together again or cut equally?): “Ring together again”, “smallest number both divide” → LCM: count in the bigger number until the smaller one divides it. “Longest equal pieces”, “greatest number of identical packs” → HCF: list the factors and pick the greatest common one. Check: the LCM is divisible by both numbers; the HCF divides both numbers.

1. 1.What is the smallest number of sweets that can be shared equally among 12 children or among 14 children, with none left over? (a) 26 (b) 85 (c) 168 (d) 84
2. 2.A teacher has 24 pencils and 56 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 4 (b) 8 (c) 32 (d) 24
3. 3.Two bells ring every 10 minutes and every 35 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 350 min (b) 5 min (c) 70 min (d) 45 min
4. 4.Two ribbons are 48 cm and 84 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 36 cm (b) 48 cm (c) 12 cm (d) 6 cm
5. 5.Two bells ring every 4 minutes and every 10 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 40 min (b) 14 min (c) 2 min (d) 20 min
6. 6.Two ribbons are 14 cm and 35 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 1 cm (b) 21 cm (c) 14 cm (d) 7 cm
7. 7.Two bells ring every 6 minutes and every 8 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 24 min (b) 48 min (c) 2 min (d) 14 min
8. 8.What is the smallest number of sweets that can be shared equally among 6 children or among 15 children, with none left over? (a) 90 (b) 21 (c) 60 (d) 30
9. 9.Two bells ring every 15 minutes and every 35 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 525 min (b) 5 min (c) 105 min (d) 50 min
10. 10.Two bells ring every 8 minutes and every 10 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 80 min (b) 18 min (c) 40 min (d) 2 min
11. 11.A teacher has 21 pencils and 28 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 21 (b) 7 (c) 84 (d) 1
12. 12.Two bells ring every 12 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 26 min (b) 168 min (c) 2 min (d) 84 min
13. 13.Two ribbons are 22 cm and 77 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 11 cm (b) 55 cm (c) 22 cm (d) 1 cm
14. 14.Two ribbons are 70 cm and 80 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 10 cm (b) 70 cm (c) 5 cm (d) 560 cm
15. 15.What is the smallest number of sweets that can be shared equally among 18 children or among 24 children, with none left over? (a) 72 (b) 432 (c) 144 (d) 42
16. 16.Two bells ring every 8 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 22 min (b) 112 min (c) 56 min (d) 2 min
17. 17.What is the smallest number of sweets that can be shared equally among 15 children or among 18 children, with none left over? (a) 180 (b) 33 (c) 270 (d) 90
18. 18.Two bells ring every 9 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 30 min (b) 189 min (c) 63 min (d) 3 min
19. 19.A teacher has 14 pencils and 21 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 14 (c) 42 (d) 7
20. 20.Two bells ring every 20 minutes and every 25 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 45 min (b) 500 min (c) 5 min (d) 100 min
21. 21.A teacher has 66 pencils and 77 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 66 (c) 11 (d) 462
22. 22.A teacher has 42 pencils and 49 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 7 (c) 294 (d) 42
23. 23.What is the smallest number of sweets that can be shared equally among 15 children or among 35 children, with none left over? (a) 50 (b) 105 (c) 210 (d) 525
24. 24.Two ribbons are 42 cm and 49 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 42 cm (b) 7 cm (c) 1 cm (d) 294 cm
25. 25.Two ribbons are 60 cm and 108 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 60 cm (b) 6 cm (c) 48 cm (d) 12 cm
26. 26.What is the smallest number of sweets that can be shared equally among 18 children or among 30 children, with none left over? (a) 90 (b) 180 (c) 540 (d) 48
27. 27.What is the smallest number of sweets that can be shared equally among 18 children or among 42 children, with none left over? (a) 60 (b) 252 (c) 756 (d) 126
28. 28.What is the smallest number of sweets that can be shared equally among 12 children or among 16 children, with none left over? (a) 96 (b) 192 (c) 48 (d) 28
29. 29.A teacher has 24 pencils and 60 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 36 (b) 24 (c) 6 (d) 12
30. 30.Two bells ring every 12 minutes and every 28 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 336 min (b) 84 min (c) 40 min (d) 4 min
31. 31.Two ribbons are 15 cm and 18 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 3 cm (b) 90 cm (c) 15 cm (d) 1 cm
32. 32.Two ribbons are 36 cm and 63 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 9 cm (b) 36 cm (c) 27 cm (d) 3 cm
33. 33.Two bells ring every 8 minutes and every 20 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 40 min (b) 4 min (c) 28 min (d) 160 min
34. 34.Two ribbons are 18 cm and 45 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 27 cm (b) 3 cm (c) 18 cm (d) 9 cm
35. 35.Two ribbons are 44 cm and 99 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 44 cm (b) 1 cm (c) 55 cm (d) 11 cm
36. 36.Two bells ring every 9 minutes and every 12 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 3 min (b) 21 min (c) 36 min (d) 108 min
37. 37.Two bells ring every 16 minutes and every 20 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 80 min (b) 36 min (c) 320 min (d) 4 min
38. 38.Two ribbons are 9 cm and 12 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 3 cm (b) 36 cm (c) 9 cm (d) 1 cm
39. 39.What is the smallest number of sweets that can be shared equally among 6 children or among 21 children, with none left over? (a) 27 (b) 42 (c) 84 (d) 126
40. 40.Two ribbons are 24 cm and 84 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 6 cm (b) 60 cm (c) 12 cm (d) 24 cm

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