HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 14 · 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 18 minutes and every 42 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 756 min (b) 60 min (c) 126 min (d) 6 min
2. 2.Two ribbons are 9 cm and 24 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 15 cm (b) 1 cm (c) 9 cm (d) 3 cm
3. 3.Two ribbons are 6 cm and 9 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 18 cm (b) 3 cm (c) 6 cm (d) 1 cm
4. 4.What is the smallest number of sweets that can be shared equally among 8 children or among 10 children, with none left over? (a) 80 (b) 40 (c) 41 (d) 18
5. 5.A teacher has 10 pencils and 35 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 10 (b) 25 (c) 1 (d) 5
6. 6.A teacher has 6 pencils and 14 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 2 (b) 8 (c) 1 (d) 6
7. 7.Two ribbons are 25 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) 5 cm (d) 15 cm
8. 8.Two ribbons are 21 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) 28 cm (b) 7 cm (c) 21 cm (d) 1 cm
9. 9.What is the smallest number of sweets that can be shared equally among 6 children or among 9 children, with none left over? (a) 36 (b) 54 (c) 15 (d) 18
10. 10.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) 270 min (c) 33 min (d) 3 min
11. 11.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) 21 min (b) 108 min (c) 3 min (d) 36 min
12. 12.Two ribbons are 16 cm and 24 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) 16 cm (c) 48 cm (d) 8 cm
13. 13.What is the smallest number of sweets that can be shared equally among 12 children or among 30 children, with none left over? (a) 120 (b) 360 (c) 60 (d) 42
14. 14.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) 4 min (b) 96 min (c) 20 min (d) 24 min
15. 15.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) 2 min (b) 40 min (c) 20 min (d) 14 min
16. 16.What is the smallest number of sweets that can be shared equally among 10 children or among 25 children, with none left over? (a) 35 (b) 50 (c) 100 (d) 250
17. 17.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) 30 (d) 60
18. 18.Two bells ring every 12 minutes and every 16 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 192 min (b) 28 min (c) 4 min (d) 48 min
19. 19.Two ribbons are 8 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) 28 cm (b) 8 cm (c) 4 cm (d) 2 cm
20. 20.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) 40 min (b) 336 min (c) 4 min (d) 84 min
21. 21.Two ribbons are 20 cm and 30 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 20 cm (b) 10 cm (c) 60 cm (d) 5 cm
22. 22.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) 3 (b) 9 (c) 18 (d) 45
23. 23.Two bells ring every 8 minutes and every 28 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 4 min (b) 36 min (c) 56 min (d) 224 min
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) 252 (b) 39 (c) 126 (d) 378
25. 25.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) 35 min (c) 5 min (d) 60 min
26. 26.Two ribbons are 36 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) 3 cm (b) 36 cm (c) 9 cm (d) 45 cm
27. 27.Two ribbons are 18 cm and 21 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 126 cm (b) 1 cm (c) 18 cm (d) 3 cm
28. 28.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) 3 min (b) 189 min (c) 63 min (d) 30 min
29. 29.Two ribbons are 30 cm and 50 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 30 cm (b) 5 cm (c) 20 cm (d) 10 cm
30. 30.What is the smallest number of sweets that can be shared equally among 6 children or among 14 children, with none left over? (a) 20 (b) 43 (c) 84 (d) 42
31. 31.A teacher has 12 pencils and 28 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 2 (b) 4 (c) 12 (d) 16
32. 32.Two ribbons are 12 cm and 21 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) 3 cm (c) 1 cm (d) 9 cm
33. 33.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) 2 min (c) 30 min (d) 60 min
34. 34.A teacher has 36 pencils and 84 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 36 (b) 12 (c) 6 (d) 48
35. 35.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) 432 min (b) 72 min (c) 42 min (d) 6 min
36. 36.What is the smallest number of sweets that can be shared equally among 9 children or among 21 children, with none left over? (a) 30 (b) 189 (c) 126 (d) 63
37. 37.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) 40 min (b) 80 min (c) 2 min (d) 18 min
38. 38.What is the smallest number of sweets that can be shared equally among 8 children or among 12 children, with none left over? (a) 96 (b) 20 (c) 48 (d) 24
39. 39.What is the smallest number of sweets that can be shared equally among 12 children or among 20 children, with none left over? (a) 60 (b) 120 (c) 32 (d) 240
40. 40.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) 3 min (b) 315 min (c) 36 min (d) 105 min

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