HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 145 · 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.Two ribbons are 15 cm and 40 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) 25 cm (c) 15 cm (d) 5 cm
2. 2.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) 2 min (b) 26 min (c) 168 min (d) 84 min
3. 3.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) 28 min (b) 40 min (c) 4 min (d) 160 min
4. 4.Two bells ring every 10 minutes and every 15 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 25 min (b) 5 min (c) 150 min (d) 30 min
5. 5.What is the smallest number of sweets that can be shared equally among 20 children or among 25 children, with none left over? (a) 500 (b) 45 (c) 200 (d) 100
6. 6.What is the smallest number of sweets that can be shared equally among 8 children or among 28 children, with none left over? (a) 224 (b) 112 (c) 56 (d) 36
7. 7.Two ribbons are 10 cm and 15 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) 1 cm (c) 5 cm (d) 30 cm
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) 30 (c) 60 (d) 21
9. 9.Two bells ring every 8 minutes and every 12 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 96 min (b) 4 min (c) 20 min (d) 24 min
10. 10.What is the smallest number of sweets that can be shared equally among 4 children or among 10 children, with none left over? (a) 21 (b) 14 (c) 40 (d) 20
11. 11.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) 2 min (b) 80 min (c) 40 min (d) 18 min
12. 12.What is the smallest number of sweets that can be shared equally among 18 children or among 42 children, with none left over? (a) 252 (b) 126 (c) 756 (d) 60
13. 13.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) 36 min (b) 21 min (c) 108 min (d) 3 min
14. 14.Two ribbons are 49 cm and 56 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) 49 cm (c) 7 cm (d) 392 cm
15. 15.Two bells ring every 25 minutes and every 30 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 750 min (b) 55 min (c) 150 min (d) 5 min
16. 16.A teacher has 4 pencils and 10 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 2 (c) 4 (d) 1
17. 17.What is the smallest number of sweets that can be shared equally among 9 children or among 12 children, with none left over? (a) 108 (b) 72 (c) 21 (d) 36
18. 18.A teacher has 36 pencils and 60 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 12 (b) 24 (c) 36 (d) 6
19. 19.Two ribbons are 30 cm and 40 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 5 cm (b) 30 cm (c) 120 cm (d) 10 cm
20. 20.Two bells ring every 6 minutes and every 15 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 90 min (b) 21 min (c) 3 min (d) 30 min
21. 21.Two ribbons are 56 cm and 64 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 4 cm (b) 448 cm (c) 8 cm (d) 56 cm
22. 22.Two bells ring every 10 minutes and every 12 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 120 min (b) 2 min (c) 22 min (d) 60 min
23. 23.Two ribbons are 16 cm and 20 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 4 cm (b) 80 cm (c) 16 cm (d) 2 cm
24. 24.What is the smallest number of sweets that can be shared equally among 18 children or among 21 children, with none left over? (a) 378 (b) 39 (c) 252 (d) 126
25. 25.Two bells ring every 10 minutes and every 25 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 250 min (b) 35 min (c) 5 min (d) 50 min
26. 26.A teacher has 50 pencils and 90 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 50 (b) 10 (c) 40 (d) 5
27. 27.Two ribbons are 6 cm and 27 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) 21 cm (c) 1 cm (d) 3 cm
28. 28.What is the smallest number of sweets that can be shared equally among 6 children or among 8 children, with none left over? (a) 48 (b) 25 (c) 24 (d) 14
29. 29.Two bells ring every 15 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 105 min (b) 3 min (c) 36 min (d) 315 min
30. 30.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) 105 min (b) 50 min (c) 5 min (d) 525 min
31. 31.Two bells ring every 12 minutes and every 42 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 54 min (b) 6 min (c) 504 min (d) 84 min
32. 32.Two bells ring every 12 minutes and every 18 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 36 min (b) 30 min (c) 216 min (d) 6 min
33. 33.Two ribbons are 12 cm and 20 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 2 cm (b) 8 cm (c) 4 cm (d) 12 cm
34. 34.Two ribbons are 24 cm and 36 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) 12 cm (c) 24 cm (d) 72 cm
35. 35.Two ribbons are 27 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) 9 cm (b) 3 cm (c) 27 cm (d) 18 cm
36. 36.Two bells ring every 4 minutes and every 6 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 24 min (b) 2 min (c) 12 min (d) 10 min
37. 37.What is the smallest number of sweets that can be shared equally among 8 children or among 14 children, with none left over? (a) 57 (b) 22 (c) 56 (d) 112
38. 38.Two ribbons are 72 cm and 81 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) 648 cm (c) 72 cm (d) 3 cm
39. 39.A teacher has 32 pencils and 72 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 4 (b) 40 (c) 8 (d) 32
40. 40.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) 2 min (b) 24 min (c) 48 min (d) 14 min

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