HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 643 · 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 15 minutes and every 18 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 270 min (b) 3 min (c) 33 min (d) 90 min
2. 2.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) 4 min (c) 160 min (d) 28 min
3. 3.Two ribbons are 20 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) 5 cm (b) 20 cm (c) 70 cm (d) 10 cm
4. 4.What is the smallest number of sweets that can be shared equally among 20 children or among 28 children, with none left over? (a) 560 (b) 48 (c) 140 (d) 280
5. 5.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) 2 min (c) 30 min (d) 16 min
6. 6.Two bells ring every 10 minutes and every 35 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 5 min (b) 45 min (c) 350 min (d) 70 min
7. 7.A teacher has 21 pencils and 49 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 21 (b) 28 (c) 7 (d) 1
8. 8.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) 48 min (b) 192 min (c) 28 min (d) 4 min
9. 9.What is the smallest number of sweets that can be shared equally among 12 children or among 16 children, with none left over? (a) 28 (b) 96 (c) 48 (d) 192
10. 10.Two bells ring every 18 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 378 min (b) 39 min (c) 126 min (d) 3 min
11. 11.Two ribbons are 35 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) 35 cm (b) 14 cm (c) 1 cm (d) 7 cm
12. 12.What is the smallest number of sweets that can be shared equally among 12 children or among 18 children, with none left over? (a) 36 (b) 72 (c) 216 (d) 30
13. 13.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) 3 min (b) 42 min (c) 27 min (d) 126 min
14. 14.A teacher has 8 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) 1 (c) 8 (d) 6
15. 15.Two ribbons are 10 cm and 14 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) 10 cm (c) 4 cm (d) 2 cm
16. 16.Two bells ring every 16 minutes and every 28 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 44 min (b) 4 min (c) 112 min (d) 448 min
17. 17.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) 135 min (b) 3 min (c) 24 min (d) 45 min
18. 18.A teacher has 30 pencils and 35 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 5 (b) 30 (c) 1 (d) 210
19. 19.A teacher has 4 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) 2 (c) 14 (d) 1
20. 20.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) 560 min (b) 4 min (c) 48 min (d) 140 min
21. 21.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) 36 min (b) 224 min (c) 56 min (d) 4 min
22. 22.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) 6 cm (b) 36 cm (c) 12 cm (d) 48 cm
23. 23.Two bells ring every 20 minutes and every 35 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 700 min (b) 5 min (c) 55 min (d) 140 min
24. 24.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) 500 min (b) 45 min (c) 100 min (d) 5 min
25. 25.Two ribbons are 15 cm and 25 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) 1 cm (c) 15 cm (d) 5 cm
26. 26.A teacher has 16 pencils and 40 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 8 (b) 24 (c) 16 (d) 4
27. 27.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) 27 min (c) 60 min (d) 3 min
28. 28.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
29. 29.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) 30 min (d) 6 min
30. 30.A teacher has 24 pencils and 36 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 12 (b) 72 (c) 6 (d) 24
31. 31.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) 2 min (b) 60 min (c) 120 min (d) 22 min
32. 32.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) 56 (c) 28 (d) 18
33. 33.Two ribbons are 36 cm and 60 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) 36 cm (c) 24 cm (d) 12 cm
34. 34.Two ribbons are 9 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) 9 cm (b) 1 cm (c) 6 cm (d) 3 cm
35. 35.What is the smallest number of sweets that can be shared equally among 12 children or among 42 children, with none left over? (a) 168 (b) 54 (c) 84 (d) 504
36. 36.What is the smallest number of sweets that can be shared equally among 10 children or among 15 children, with none left over? (a) 60 (b) 30 (c) 150 (d) 25
37. 37.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
38. 38.A teacher has 63 pencils and 81 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) 63 (d) 18
39. 39.Two bells ring every 12 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 2 min (b) 168 min (c) 84 min (d) 26 min
40. 40.Two ribbons are 6 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) 1 cm (b) 6 cm (c) 9 cm (d) 3 cm

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