HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 799 · 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 8 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 24 min (b) 14 min (c) 2 min (d) 48 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) 24 min (b) 135 min (c) 3 min (d) 45 min
3. 3.What is the smallest number of sweets that can be shared equally among 18 children or among 21 children, with none left over? (a) 39 (b) 378 (c) 252 (d) 126
4. 4.What is the smallest number of sweets that can be shared equally among 10 children or among 14 children, with none left over? (a) 70 (b) 24 (c) 140 (d) 71
5. 5.Two ribbons are 33 cm and 88 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 55 cm (b) 1 cm (c) 11 cm (d) 33 cm
6. 6.Two ribbons are 14 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) 1 cm (b) 14 cm (c) 2 cm (d) 4 cm
7. 7.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) 24 min (c) 70 min (d) 2 min
8. 8.Two ribbons are 60 cm and 96 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) 6 cm (c) 36 cm (d) 60 cm
9. 9.What is the smallest number of sweets that can be shared equally among 12 children or among 30 children, with none left over? (a) 42 (b) 60 (c) 360 (d) 120
10. 10.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) 63 (c) 189 (d) 126
11. 11.Two ribbons are 12 cm and 16 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) 48 cm (d) 2 cm
12. 12.Two ribbons are 28 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) 224 cm (b) 28 cm (c) 4 cm (d) 2 cm
13. 13.Two ribbons are 16 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) 40 cm (b) 8 cm (c) 4 cm (d) 16 cm
14. 14.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) 6 min (b) 54 min (c) 84 min (d) 504 min
15. 15.A teacher has 20 pencils and 50 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 10 (b) 30 (c) 20 (d) 5
16. 16.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) 126 min (c) 60 min (d) 6 min
17. 17.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
18. 18.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) 60 min (b) 30 min (c) 16 min (d) 2 min
19. 19.A teacher has 55 pencils and 66 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 330 (c) 55 (d) 11
20. 20.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) 2 min (b) 24 min (c) 12 min (d) 10 min
21. 21.A teacher has 24 pencils and 64 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 8 (b) 40 (c) 4 (d) 24
22. 22.Two bells ring every 6 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 20 min (b) 2 min (c) 84 min (d) 42 min
23. 23.What is the smallest number of sweets that can be shared equally among 24 children or among 30 children, with none left over? (a) 240 (b) 120 (c) 54 (d) 720
24. 24.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) 1 cm (b) 22 cm (c) 11 cm (d) 55 cm
25. 25.Two bells ring every 20 minutes and every 28 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 4 min (b) 48 min (c) 140 min (d) 560 min
26. 26.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) 40 min (c) 18 min (d) 2 min
27. 27.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) 320 min (b) 36 min (c) 4 min (d) 80 min
28. 28.Two ribbons are 28 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) 28 cm (b) 7 cm (c) 140 cm (d) 1 cm
29. 29.Two ribbons are 16 cm and 72 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) 8 cm (d) 56 cm
30. 30.Two ribbons are 8 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) 40 cm (b) 8 cm (c) 2 cm (d) 1 cm
31. 31.Two ribbons are 24 cm and 54 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 24 cm (b) 3 cm (c) 30 cm (d) 6 cm
32. 32.A teacher has 45 pencils and 72 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 27 (b) 3 (c) 9 (d) 45
33. 33.What is the smallest number of sweets that can be shared equally among 12 children or among 20 children, with none left over? (a) 120 (b) 60 (c) 240 (d) 32
34. 34.What is the smallest number of sweets that can be shared equally among 12 children or among 42 children, with none left over? (a) 54 (b) 504 (c) 84 (d) 168
35. 35.What is the smallest number of sweets that can be shared equally among 4 children or among 14 children, with none left over? (a) 29 (b) 28 (c) 18 (d) 56
36. 36.A teacher has 4 pencils and 6 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) 1
37. 37.Two ribbons are 36 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) 6 cm (d) 12 cm
38. 38.What is the smallest number of sweets that can be shared equally among 10 children or among 35 children, with none left over? (a) 140 (b) 70 (c) 45 (d) 350
39. 39.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) 36 (c) 72 (d) 21
40. 40.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) 3 min (c) 108 min (d) 36 min

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