HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 547 · 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 28 pencils and 36 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 2 (b) 4 (c) 8 (d) 28
2. 2.What is the smallest number of sweets that can be shared equally among 10 children or among 35 children, with none left over? (a) 140 (b) 45 (c) 70 (d) 350
3. 3.Two bells ring every 9 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 3 min (b) 189 min (c) 30 min (d) 63 min
4. 4.What is the smallest number of sweets that can be shared equally among 9 children or among 12 children, with none left over? (a) 72 (b) 108 (c) 36 (d) 21
5. 5.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) 3 min (c) 315 min (d) 105 min
6. 6.Two ribbons are 20 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) 50 cm (b) 5 cm (c) 20 cm (d) 10 cm
7. 7.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) 55 min (c) 140 min (d) 5 min
8. 8.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) 15 min (c) 3 min (d) 54 min
9. 9.A teacher has 6 pencils and 8 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 24 (b) 6 (c) 1 (d) 2
10. 10.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) 24 min (b) 4 min (c) 20 min (d) 96 min
11. 11.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) 150 (c) 25 (d) 30
12. 12.What is the smallest number of sweets that can be shared equally among 10 children or among 14 children, with none left over? (a) 70 (b) 71 (c) 140 (d) 24
13. 13.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) 10 (b) 120 (c) 5 (d) 30
14. 14.Two bells ring every 8 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 2 min (b) 112 min (c) 22 min (d) 56 min
15. 15.What is the smallest number of sweets that can be shared equally among 18 children or among 42 children, with none left over? (a) 252 (b) 756 (c) 60 (d) 126
16. 16.What is the smallest number of sweets that can be shared equally among 25 children or among 30 children, with none left over? (a) 300 (b) 55 (c) 750 (d) 150
17. 17.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) 10 min (b) 12 min (c) 24 min (d) 2 min
18. 18.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) 70 min (d) 350 min
19. 19.What is the smallest number of sweets that can be shared equally among 10 children or among 12 children, with none left over? (a) 22 (b) 60 (c) 61 (d) 120
20. 20.What is the smallest number of sweets that can be shared equally among 12 children or among 20 children, with none left over? (a) 32 (b) 120 (c) 60 (d) 240
21. 21.A teacher has 22 pencils and 77 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) 55 (d) 11
22. 22.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) 504 min (c) 54 min (d) 84 min
23. 23.Two ribbons are 20 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) 1 cm (b) 20 cm (c) 25 cm (d) 5 cm
24. 24.Two bells ring every 15 minutes and every 25 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 75 min (b) 40 min (c) 375 min (d) 5 min
25. 25.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) 7 (b) 1 (c) 21 (d) 28
26. 26.Two ribbons are 20 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) 20 cm (b) 1 cm (c) 100 cm (d) 5 cm
27. 27.Two ribbons are 49 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) 1 cm (b) 49 cm (c) 392 cm (d) 7 cm
28. 28.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) 3 cm (b) 6 cm (c) 1 cm (d) 21 cm
29. 29.A teacher has 24 pencils and 28 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 168 (b) 24 (c) 4 (d) 2
30. 30.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) 336 min (b) 4 min (c) 84 min (d) 40 min
31. 31.A teacher has 21 pencils and 27 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 21 (b) 3 (c) 1 (d) 6
32. 32.What is the smallest number of sweets that can be shared equally among 24 children or among 30 children, with none left over? (a) 120 (b) 240 (c) 720 (d) 54
33. 33.What is the smallest number of sweets that can be shared equally among 8 children or among 20 children, with none left over? (a) 160 (b) 28 (c) 80 (d) 40
34. 34.A teacher has 10 pencils and 18 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 8 (c) 2 (d) 10
35. 35.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) 105 min (b) 50 min (c) 5 min (d) 525 min
36. 36.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) 45 min (c) 24 min (d) 3 min
37. 37.What is the smallest number of sweets that can be shared equally among 6 children or among 9 children, with none left over? (a) 54 (b) 36 (c) 15 (d) 18
38. 38.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) 48 cm (c) 12 cm (d) 36 cm
39. 39.What is the smallest number of sweets that can be shared equally among 20 children or among 25 children, with none left over? (a) 100 (b) 200 (c) 500 (d) 45
40. 40.Two ribbons are 4 cm and 6 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) 4 cm (d) 2 cm

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