HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 226 · 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 15 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 3 min (b) 30 min (c) 90 min (d) 21 min
2. 2.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) 27 cm (b) 9 cm (c) 3 cm (d) 36 cm
3. 3.Two ribbons are 44 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) 44 cm (b) 1 cm (c) 33 cm (d) 11 cm
4. 4.A teacher has 36 pencils and 81 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 36 (b) 45 (c) 3 (d) 9
5. 5.Two ribbons are 66 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) 66 cm (b) 11 cm (c) 462 cm (d) 1 cm
6. 6.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) 54 min (b) 3 min (c) 15 min (d) 18 min
7. 7.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) 5 min (b) 55 min (c) 150 min (d) 750 min
8. 8.Two ribbons are 60 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) 48 cm (b) 6 cm (c) 12 cm (d) 60 cm
9. 9.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) 21 cm (c) 1 cm (d) 7 cm
10. 10.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
11. 11.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) 8 cm (d) 16 cm
12. 12.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) 90 (c) 45 (d) 135
13. 13.Two ribbons are 12 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) 3 cm (b) 60 cm (c) 1 cm (d) 12 cm
14. 14.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) 648 cm (b) 3 cm (c) 72 cm (d) 9 cm
15. 15.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) 2 min (b) 30 min (c) 16 min (d) 60 min
16. 16.Two ribbons are 24 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) 3 cm (b) 120 cm (c) 6 cm (d) 24 cm
17. 17.Two ribbons are 30 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) 5 cm (b) 10 cm (c) 30 cm (d) 40 cm
18. 18.What is the smallest number of sweets that can be shared equally among 8 children or among 28 children, with none left over? (a) 56 (b) 224 (c) 36 (d) 112
19. 19.What is the smallest number of sweets that can be shared equally among 12 children or among 42 children, with none left over? (a) 504 (b) 84 (c) 54 (d) 168
20. 20.A teacher has 14 pencils and 18 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 4 (b) 14 (c) 2 (d) 1
21. 21.Two ribbons are 22 cm and 33 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 11 cm (b) 22 cm (c) 1 cm (d) 66 cm
22. 22.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) 24 min (d) 96 min
23. 23.What is the smallest number of sweets that can be shared equally among 16 children or among 20 children, with none left over? (a) 320 (b) 160 (c) 36 (d) 80
24. 24.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) 2 min (b) 20 min (c) 42 min (d) 84 min
25. 25.Two ribbons are 40 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) 24 cm (b) 40 cm (c) 8 cm (d) 4 cm
26. 26.A teacher has 24 pencils and 56 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 4 (b) 32 (c) 8 (d) 24
27. 27.Two ribbons are 22 cm and 55 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 33 cm (b) 22 cm (c) 11 cm (d) 1 cm
28. 28.A teacher has 30 pencils and 40 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 120 (b) 5 (c) 30 (d) 10
29. 29.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) 6 min (d) 432 min
30. 30.Two bells ring every 12 minutes and every 20 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 32 min (b) 4 min (c) 60 min (d) 240 min
31. 31.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) 6 min (b) 60 min (c) 360 min (d) 42 min
32. 32.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) 84 min (d) 504 min
33. 33.A teacher has 8 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) 8 (c) 20 (d) 4
34. 34.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) 24 (b) 40 (c) 4 (d) 8
35. 35.A teacher has 22 pencils and 55 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 22 (b) 1 (c) 11 (d) 33
36. 36.A teacher has 12 pencils and 42 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 12 (b) 6 (c) 3 (d) 30
37. 37.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) 525 min (d) 5 min
38. 38.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) 50 min (b) 5 min (c) 35 min (d) 250 min
39. 39.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) 4 cm (b) 2 cm (c) 1 cm (d) 6 cm
40. 40.A teacher has 9 pencils and 12 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 9 (b) 36 (c) 3 (d) 1

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