HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 436 · 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 12 cm and 42 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) 3 cm (c) 30 cm (d) 12 cm
2. 2.Two ribbons are 9 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) 1 cm (b) 12 cm (c) 9 cm (d) 3 cm
3. 3.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) 2 min (b) 40 min (c) 80 min (d) 18 min
4. 4.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) 30 min (b) 21 min (c) 90 min (d) 3 min
5. 5.Two bells ring every 12 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 252 min (b) 33 min (c) 3 min (d) 84 min
6. 6.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) 36 min (d) 108 min
7. 7.Two ribbons are 77 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) 22 cm (b) 77 cm (c) 11 cm (d) 1 cm
8. 8.Two ribbons are 18 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) 72 cm (b) 6 cm (c) 3 cm (d) 18 cm
9. 9.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) 84 min (c) 4 min (d) 336 min
10. 10.A teacher has 14 pencils and 35 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 7 (b) 1 (c) 14 (d) 21
11. 11.A teacher has 8 pencils and 18 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 8 (b) 10 (c) 1 (d) 2
12. 12.A teacher has 30 pencils and 36 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 30 (c) 6 (d) 180
13. 13.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) 1 (b) 10 (c) 25 (d) 5
14. 14.Two bells ring every 8 minutes and every 20 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 40 min (b) 28 min (c) 160 min (d) 4 min
15. 15.Two bells ring every 12 minutes and every 15 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 180 min (b) 3 min (c) 60 min (d) 27 min
16. 16.What is the smallest number of sweets that can be shared equally among 6 children or among 21 children, with none left over? (a) 27 (b) 84 (c) 126 (d) 42
17. 17.What is the smallest number of sweets that can be shared equally among 12 children or among 15 children, with none left over? (a) 180 (b) 120 (c) 60 (d) 27
18. 18.What is the smallest number of sweets that can be shared equally among 4 children or among 6 children, with none left over? (a) 24 (b) 10 (c) 12 (d) 13
19. 19.A teacher has 8 pencils and 20 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) 12 (d) 4
20. 20.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) 5 min (b) 525 min (c) 50 min (d) 105 min
21. 21.Two ribbons are 12 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) 1 cm (b) 12 cm (c) 3 cm (d) 15 cm
22. 22.A teacher has 9 pencils and 21 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 9 (b) 1 (c) 12 (d) 3
23. 23.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) 11 cm (b) 1 cm (c) 66 cm (d) 462 cm
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) 42 min (b) 2 min (c) 84 min (d) 20 min
25. 25.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) 4 min (b) 48 min (c) 28 min (d) 192 min
26. 26.What is the smallest number of sweets that can be shared equally among 9 children or among 15 children, with none left over? (a) 90 (b) 24 (c) 45 (d) 135
27. 27.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) 3 cm (d) 15 cm
28. 28.What is the smallest number of sweets that can be shared equally among 18 children or among 24 children, with none left over? (a) 42 (b) 432 (c) 144 (d) 72
29. 29.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) 42 min (b) 3 min (c) 27 min (d) 126 min
30. 30.Two ribbons are 20 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) 2 cm (b) 16 cm (c) 4 cm (d) 20 cm
31. 31.Two ribbons are 18 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) 9 cm (b) 3 cm (c) 54 cm (d) 18 cm
32. 32.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) 20 (d) 96
33. 33.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) 150 min (b) 25 min (c) 30 min (d) 5 min
34. 34.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) 24 cm (c) 120 cm (d) 6 cm
35. 35.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) 18 min (b) 3 min (c) 54 min (d) 15 min
36. 36.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) 36 min (b) 216 min (c) 6 min (d) 30 min
37. 37.A teacher has 12 pencils and 20 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 4 (b) 12 (c) 2 (d) 8
38. 38.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) 224 min (d) 56 min
39. 39.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) 33 min (b) 3 min (c) 90 min (d) 270 min
40. 40.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) 5 (b) 10 (c) 120 (d) 30

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