HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 278 · 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 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) 2 cm (b) 6 cm (c) 4 cm (d) 1 cm
2. 2.A teacher has 48 pencils and 56 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 48 (b) 4 (c) 8 (d) 336
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) 80 min (b) 18 min (c) 2 min (d) 40 min
4. 4.A teacher has 60 pencils and 72 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 60 (b) 6 (c) 360 (d) 12
5. 5.A teacher has 36 pencils and 45 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 180 (c) 9 (d) 36
6. 6.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) 60 min (b) 4 min (c) 240 min (d) 32 min
7. 7.Two bells ring every 4 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) 14 min (d) 20 min
8. 8.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) 24 min (b) 140 min (c) 2 min (d) 70 min
9. 9.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
10. 10.Two ribbons are 24 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) 12 cm (b) 6 cm (c) 84 cm (d) 24 cm
11. 11.Two ribbons are 6 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) 21 cm (b) 1 cm (c) 3 cm (d) 6 cm
12. 12.A teacher has 15 pencils and 25 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 15 (b) 10 (c) 5 (d) 1
13. 13.Two ribbons are 22 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) 1 cm (b) 77 cm (c) 22 cm (d) 11 cm
14. 14.A teacher has 18 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) 6 (d) 18
15. 15.What is the smallest number of sweets that can be shared equally among 18 children or among 30 children, with none left over? (a) 48 (b) 90 (c) 540 (d) 180
16. 16.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) 14 cm (b) 2 cm (c) 1 cm (d) 4 cm
17. 17.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) 560 min (d) 140 min
18. 18.What is the smallest number of sweets that can be shared equally among 15 children or among 21 children, with none left over? (a) 36 (b) 315 (c) 105 (d) 210
19. 19.What is the smallest number of sweets that can be shared equally among 20 children or among 35 children, with none left over? (a) 700 (b) 55 (c) 140 (d) 280
20. 20.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) 6 cm (b) 9 cm (c) 3 cm (d) 1 cm
21. 21.Two ribbons are 35 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) 1 cm (b) 35 cm (c) 210 cm (d) 7 cm
22. 22.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) 90 min (c) 3 min (d) 21 min
23. 23.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) 1 cm (b) 33 cm (c) 22 cm (d) 11 cm
24. 24.Two ribbons are 33 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) 44 cm (d) 33 cm
25. 25.What is the smallest number of sweets that can be shared equally among 20 children or among 24 children, with none left over? (a) 120 (b) 240 (c) 480 (d) 44
26. 26.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) 168 (c) 84 (d) 504
27. 27.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) 3 min (c) 18 min (d) 54 min
28. 28.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) 6 min (c) 216 min (d) 30 min
29. 29.Two ribbons are 63 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) 63 cm (b) 3 cm (c) 9 cm (d) 504 cm
30. 30.What is the smallest number of sweets that can be shared equally among 12 children or among 21 children, with none left over? (a) 168 (b) 33 (c) 84 (d) 252
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) 120 min (b) 22 min (c) 60 min (d) 2 min
32. 32.What is the smallest number of sweets that can be shared equally among 10 children or among 14 children, with none left over? (a) 140 (b) 71 (c) 24 (d) 70
33. 33.Two bells ring every 15 minutes and every 20 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 300 min (b) 35 min (c) 60 min (d) 5 min
34. 34.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) 5 min (c) 30 min (d) 25 min
35. 35.Two ribbons are 32 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) 8 cm (b) 4 cm (c) 32 cm (d) 40 cm
36. 36.Two bells ring every 4 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 18 min (b) 56 min (c) 28 min (d) 2 min
37. 37.Two ribbons are 36 cm and 45 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) 36 cm (c) 180 cm (d) 9 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) 3 min (b) 108 min (c) 21 min (d) 36 min
39. 39.Two ribbons are 8 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) 6 cm (c) 2 cm (d) 8 cm
40. 40.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

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