HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 985 · 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.A teacher has 14 pencils and 49 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 7 (c) 35 (d) 14
2. 2.Two ribbons are 27 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) 27 cm (b) 3 cm (c) 45 cm (d) 9 cm
3. 3.What is the smallest number of sweets that can be shared equally among 10 children or among 14 children, with none left over? (a) 71 (b) 24 (c) 140 (d) 70
4. 4.Two ribbons are 4 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) 2 cm (b) 14 cm (c) 4 cm (d) 1 cm
5. 5.Two ribbons are 27 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) 18 cm (b) 3 cm (c) 27 cm (d) 9 cm
6. 6.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) 84 min (c) 2 min (d) 20 min
7. 7.What is the smallest number of sweets that can be shared equally among 12 children or among 30 children, with none left over? (a) 60 (b) 42 (c) 360 (d) 120
8. 8.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) 56 min (c) 4 min (d) 224 min
9. 9.A teacher has 6 pencils and 9 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 18 (c) 1 (d) 6
10. 10.A teacher has 80 pencils and 90 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 5 (b) 720 (c) 10 (d) 80
11. 11.Two ribbons are 28 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) 35 cm (b) 1 cm (c) 7 cm (d) 28 cm
12. 12.What is the smallest number of sweets that can be shared equally among 9 children or among 12 children, with none left over? (a) 21 (b) 72 (c) 108 (d) 36
13. 13.Two bells ring every 16 minutes and every 20 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 36 min (b) 80 min (c) 320 min (d) 4 min
14. 14.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) 35 min (b) 60 min (c) 300 min (d) 5 min
15. 15.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) 54 min (c) 15 min (d) 3 min
16. 16.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) 48 min (c) 4 min (d) 140 min
17. 17.What is the smallest number of sweets that can be shared equally among 6 children or among 21 children, with none left over? (a) 126 (b) 27 (c) 42 (d) 84
18. 18.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) 216 min (b) 30 min (c) 6 min (d) 36 min
19. 19.What is the smallest number of sweets that can be shared equally among 4 children or among 10 children, with none left over? (a) 21 (b) 40 (c) 14 (d) 20
20. 20.Two ribbons are 12 cm and 54 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) 42 cm (d) 3 cm
21. 21.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
22. 22.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) 60 min (c) 4 min (d) 240 min
23. 23.What is the smallest number of sweets that can be shared equally among 18 children or among 24 children, with none left over? (a) 144 (b) 72 (c) 432 (d) 42
24. 24.A teacher has 56 pencils and 64 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 4 (b) 56 (c) 448 (d) 8
25. 25.What is the smallest number of sweets that can be shared equally among 18 children or among 21 children, with none left over? (a) 39 (b) 378 (c) 126 (d) 252
26. 26.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) 4 cm (c) 24 cm (d) 8 cm
27. 27.Two ribbons are 48 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) 12 cm (b) 6 cm (c) 36 cm (d) 48 cm
28. 28.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) 36 min (b) 105 min (c) 315 min (d) 3 min
29. 29.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) 4 min (b) 96 min (c) 24 min (d) 20 min
30. 30.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) 39 min (b) 126 min (c) 378 min (d) 3 min
31. 31.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) 21 (b) 1 (c) 14 (d) 7
32. 32.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) 32 (b) 24 (c) 4 (d) 8
33. 33.Two ribbons are 12 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) 12 cm (b) 6 cm (c) 3 cm (d) 36 cm
34. 34.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) 28 min (b) 4 min (c) 48 min (d) 192 min
35. 35.What is the smallest number of sweets that can be shared equally among 10 children or among 15 children, with none left over? (a) 150 (b) 25 (c) 60 (d) 30
36. 36.Two ribbons are 54 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) 9 cm (b) 378 cm (c) 3 cm (d) 54 cm
37. 37.Two ribbons are 15 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) 15 cm (b) 25 cm (c) 5 cm (d) 1 cm
38. 38.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) 7 cm (c) 1 cm (d) 14 cm
39. 39.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) 25 min (d) 30 min
40. 40.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) 35 min (b) 50 min (c) 5 min (d) 250 min

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