HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 721 · 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 bells ring every 6 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 3 min (b) 27 min (c) 42 min (d) 126 min
2. 2.Two bells ring every 9 minutes and every 15 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 45 min (b) 135 min (c) 3 min (d) 24 min
3. 3.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) 10 min (c) 12 min (d) 2 min
4. 4.Two bells ring every 6 minutes and every 9 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 15 min (b) 54 min (c) 18 min (d) 3 min
5. 5.Two bells ring every 15 minutes and every 25 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 375 min (b) 75 min (c) 5 min (d) 40 min
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) 112 (b) 36 (c) 224 (d) 56
7. 7.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
8. 8.Two bells ring every 6 minutes and every 10 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 16 min (b) 60 min (c) 2 min (d) 30 min
9. 9.What is the smallest number of sweets that can be shared equally among 10 children or among 25 children, with none left over? (a) 250 (b) 35 (c) 100 (d) 50
10. 10.A teacher has 36 pencils and 45 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 9 (b) 3 (c) 180 (d) 36
11. 11.What is the smallest number of sweets that can be shared equally among 8 children or among 10 children, with none left over? (a) 18 (b) 41 (c) 40 (d) 80
12. 12.What is the smallest number of sweets that can be shared equally among 15 children or among 20 children, with none left over? (a) 35 (b) 60 (c) 120 (d) 300
13. 13.What is the smallest number of sweets that can be shared equally among 9 children or among 15 children, with none left over? (a) 24 (b) 135 (c) 90 (d) 45
14. 14.Two bells ring every 10 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 140 min (b) 2 min (c) 70 min (d) 24 min
15. 15.Two bells ring every 18 minutes and every 24 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 42 min (b) 72 min (c) 432 min (d) 6 min
16. 16.What is the smallest number of sweets that can be shared equally among 10 children or among 14 children, with none left over? (a) 24 (b) 140 (c) 70 (d) 71
17. 17.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) 3 cm (b) 36 cm (c) 27 cm (d) 9 cm
18. 18.What is the smallest number of sweets that can be shared equally among 10 children or among 12 children, with none left over? (a) 60 (b) 120 (c) 61 (d) 22
19. 19.Two bells ring every 15 minutes and every 18 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 90 min (b) 33 min (c) 270 min (d) 3 min
20. 20.Two ribbons are 22 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) 1 cm (b) 77 cm (c) 22 cm (d) 11 cm
21. 21.What is the smallest number of sweets that can be shared equally among 12 children or among 30 children, with none left over? (a) 360 (b) 120 (c) 42 (d) 60
22. 22.What is the smallest number of sweets that can be shared equally among 8 children or among 20 children, with none left over? (a) 160 (b) 28 (c) 40 (d) 80
23. 23.Two ribbons are 25 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) 5 cm (c) 25 cm (d) 10 cm
24. 24.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) 6 min (b) 36 min (c) 30 min (d) 216 min
25. 25.Two ribbons are 27 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) 3 cm (d) 27 cm
26. 26.Two ribbons are 4 cm and 10 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) 4 cm (c) 1 cm (d) 2 cm
27. 27.What is the smallest number of sweets that can be shared equally among 20 children or among 25 children, with none left over? (a) 200 (b) 45 (c) 100 (d) 500
28. 28.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) 30 min (c) 5 min (d) 150 min
29. 29.A teacher has 45 pencils and 63 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 45 (b) 18 (c) 9 (d) 3
30. 30.A teacher has 20 pencils and 25 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 100 (b) 20 (c) 5 (d) 1
31. 31.Two ribbons are 6 cm and 10 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) 4 cm (c) 6 cm (d) 1 cm
32. 32.Two ribbons are 16 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) 16 cm (b) 1 cm (c) 2 cm (d) 144 cm
33. 33.Two ribbons are 18 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) 63 cm (b) 18 cm (c) 3 cm (d) 9 cm
34. 34.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) 14 (c) 24 (d) 25
35. 35.A teacher has 63 pencils and 81 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 63 (b) 9 (c) 18 (d) 3
36. 36.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) 112 (c) 56 (d) 22
37. 37.Two bells ring every 15 minutes and every 20 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 300 min (b) 5 min (c) 60 min (d) 35 min
38. 38.Two ribbons are 12 cm and 32 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) 12 cm (c) 2 cm (d) 20 cm
39. 39.What is the smallest number of sweets that can be shared equally among 4 children or among 14 children, with none left over? (a) 18 (b) 56 (c) 29 (d) 28
40. 40.Two ribbons are 84 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) 12 cm (b) 24 cm (c) 84 cm (d) 6 cm

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