HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 940 · 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 50 cm and 90 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 50 cm (b) 5 cm (c) 10 cm (d) 40 cm
2. 2.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) 22 min (b) 60 min (c) 120 min (d) 2 min
3. 3.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) 5 min (b) 100 min (c) 45 min (d) 500 min
4. 4.A teacher has 60 pencils and 96 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 36 (b) 60 (c) 12 (d) 6
5. 5.Two ribbons are 15 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) 12 cm (b) 1 cm (c) 15 cm (d) 3 cm
6. 6.What is the smallest number of sweets that can be shared equally among 16 children or among 28 children, with none left over? (a) 448 (b) 224 (c) 44 (d) 112
7. 7.A teacher has 25 pencils and 40 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 15 (b) 1 (c) 25 (d) 5
8. 8.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) 56 (c) 22 (d) 112
9. 9.A teacher has 35 pencils and 45 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 10 (b) 35 (c) 5 (d) 1
10. 10.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) 30 min (c) 216 min (d) 36 min
11. 11.Two ribbons are 16 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) 16 cm (b) 24 cm (c) 4 cm (d) 8 cm
12. 12.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) 3 min (b) 21 min (c) 30 min (d) 90 min
13. 13.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) 1 cm (b) 16 cm (c) 144 cm (d) 2 cm
14. 14.A teacher has 18 pencils and 24 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 3 (c) 72 (d) 18
15. 15.Two ribbons are 24 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) 24 cm (c) 40 cm (d) 8 cm
16. 16.What is the smallest number of sweets that can be shared equally among 18 children or among 42 children, with none left over? (a) 126 (b) 60 (c) 756 (d) 252
17. 17.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) 3 cm (b) 9 cm (c) 63 cm (d) 18 cm
18. 18.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
19. 19.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
20. 20.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) 3 min (b) 270 min (c) 33 min (d) 90 min
21. 21.Two ribbons are 8 cm and 28 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) 8 cm (c) 2 cm (d) 4 cm
22. 22.Two ribbons are 21 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) 21 cm (b) 1 cm (c) 14 cm (d) 7 cm
23. 23.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) 20 min (b) 4 min (c) 96 min (d) 24 min
24. 24.Two ribbons are 14 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) 2 cm (b) 1 cm (c) 112 cm (d) 14 cm
25. 25.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) 105 min (c) 36 min (d) 315 min
26. 26.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) 50 min (b) 105 min (c) 5 min (d) 525 min
27. 27.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) 1 (b) 4 (c) 2 (d) 12
28. 28.Two bells ring every 12 minutes and every 30 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 42 min (b) 60 min (c) 360 min (d) 6 min
29. 29.Two ribbons are 50 cm and 70 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) 5 cm (c) 50 cm (d) 20 cm
30. 30.A teacher has 24 pencils and 84 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 24 (b) 6 (c) 12 (d) 60
31. 31.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) 3 min (b) 135 min (c) 24 min (d) 45 min
32. 32.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) 45 (d) 90
33. 33.Two ribbons are 24 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) 4 cm (b) 24 cm (c) 16 cm (d) 8 cm
34. 34.A teacher has 12 pencils and 30 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 12 (c) 18 (d) 6
35. 35.Two ribbons are 50 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) 50 cm (b) 10 cm (c) 30 cm (d) 5 cm
36. 36.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
37. 37.Two ribbons are 20 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) 15 cm (d) 20 cm
38. 38.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) 108 min (c) 3 min (d) 21 min
39. 39.A teacher has 20 pencils and 24 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 120 (b) 20 (c) 4 (d) 2
40. 40.What is the smallest number of sweets that can be shared equally among 8 children or among 12 children, with none left over? (a) 24 (b) 48 (c) 96 (d) 20

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