HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 709 · 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.What is the smallest number of sweets that can be shared equally among 12 children or among 28 children, with none left over? (a) 40 (b) 336 (c) 168 (d) 84
2. 2.What is the smallest number of sweets that can be shared equally among 12 children or among 42 children, with none left over? (a) 84 (b) 168 (c) 54 (d) 504
3. 3.Two ribbons are 21 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) 35 cm (c) 21 cm (d) 7 cm
4. 4.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) 22 min (b) 2 min (c) 112 min (d) 56 min
5. 5.What is the smallest number of sweets that can be shared equally among 10 children or among 15 children, with none left over? (a) 25 (b) 30 (c) 60 (d) 150
6. 6.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) 84 min (b) 40 min (c) 4 min (d) 336 min
7. 7.Two ribbons are 45 cm and 81 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) 9 cm (d) 45 cm
8. 8.Two ribbons are 30 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) 30 cm (b) 1 cm (c) 210 cm (d) 5 cm
9. 9.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) 27 min (b) 126 min (c) 3 min (d) 42 min
10. 10.A teacher has 55 pencils and 88 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 55 (c) 11 (d) 33
11. 11.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) 24 min (b) 45 min (c) 3 min (d) 135 min
12. 12.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) 20 min (d) 84 min
13. 13.Two ribbons are 24 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) 8 cm (b) 24 cm (c) 4 cm (d) 32 cm
14. 14.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) 30 min (b) 150 min (c) 5 min (d) 25 min
15. 15.What is the smallest number of sweets that can be shared equally among 8 children or among 12 children, with none left over? (a) 48 (b) 96 (c) 20 (d) 24
16. 16.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) 50 min (b) 250 min (c) 35 min (d) 5 min
17. 17.A teacher has 21 pencils and 35 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 14 (b) 21 (c) 7 (d) 1
18. 18.Two bells ring every 25 minutes and every 30 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 150 min (b) 55 min (c) 5 min (d) 750 min
19. 19.Two ribbons are 20 cm and 50 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) 30 cm (d) 10 cm
20. 20.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) 45 min (b) 5 min (c) 100 min (d) 500 min
21. 21.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
22. 22.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) 70 min (b) 5 min (c) 45 min (d) 350 min
23. 23.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) 315 min (c) 105 min (d) 3 min
24. 24.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) 40 min (b) 80 min (c) 18 min (d) 2 min
25. 25.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) 5 min (c) 300 min (d) 60 min
26. 26.Two ribbons are 16 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) 16 cm (b) 4 cm (c) 8 cm (d) 48 cm
27. 27.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) 27 (c) 60 (d) 120
28. 28.What is the smallest number of sweets that can be shared equally among 10 children or among 35 children, with none left over? (a) 45 (b) 70 (c) 140 (d) 350
29. 29.Two ribbons are 22 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) 22 cm (b) 55 cm (c) 1 cm (d) 11 cm
30. 30.Two ribbons are 20 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) 15 cm (b) 20 cm (c) 1 cm (d) 5 cm
31. 31.What is the smallest number of sweets that can be shared equally among 15 children or among 25 children, with none left over? (a) 375 (b) 150 (c) 75 (d) 40
32. 32.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) 2 min (c) 140 min (d) 70 min
33. 33.Two ribbons are 32 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) 32 cm (b) 24 cm (c) 8 cm (d) 4 cm
34. 34.What is the smallest number of sweets that can be shared equally among 9 children or among 21 children, with none left over? (a) 189 (b) 30 (c) 63 (d) 126
35. 35.What is the smallest number of sweets that can be shared equally among 12 children or among 16 children, with none left over? (a) 48 (b) 28 (c) 192 (d) 96
36. 36.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) 504 min (d) 84 min
37. 37.A teacher has 32 pencils and 56 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 24 (b) 4 (c) 8 (d) 32
38. 38.A teacher has 64 pencils and 72 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 576 (b) 4 (c) 64 (d) 8
39. 39.A teacher has 6 pencils and 16 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 6 (c) 2 (d) 10
40. 40.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) 140 (c) 24 (d) 71

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