HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 119 · 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 18 children or among 21 children, with none left over? (a) 378 (b) 39 (c) 252 (d) 126
2. 2.Two ribbons are 40 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) 5 cm (b) 360 cm (c) 40 cm (d) 1 cm
3. 3.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) 4 min (b) 40 min (c) 336 min (d) 84 min
4. 4.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) 84 min (b) 2 min (c) 20 min (d) 42 min
5. 5.What is the smallest number of sweets that can be shared equally among 15 children or among 18 children, with none left over? (a) 90 (b) 180 (c) 270 (d) 33
6. 6.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) 28 (c) 56 (d) 18
7. 7.What is the smallest number of sweets that can be shared equally among 18 children or among 30 children, with none left over? (a) 90 (b) 540 (c) 180 (d) 48
8. 8.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
9. 9.Two ribbons are 10 cm and 12 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) 60 cm (c) 10 cm (d) 2 cm
10. 10.Two bells ring every 24 minutes and every 30 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 6 min (b) 54 min (c) 120 min (d) 720 min
11. 11.A teacher has 42 pencils and 49 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 294 (b) 7 (c) 1 (d) 42
12. 12.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) 56 min (b) 18 min (c) 28 min (d) 2 min
13. 13.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) 56 (b) 4 (c) 448 (d) 8
14. 14.Two ribbons are 88 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) 792 cm (c) 11 cm (d) 88 cm
15. 15.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) 192 min (b) 48 min (c) 28 min (d) 4 min
16. 16.Two ribbons are 21 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) 3 cm (c) 1 cm (d) 6 cm
17. 17.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) 4 min (b) 224 min (c) 56 min (d) 36 min
18. 18.A teacher has 20 pencils and 50 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 10 (b) 20 (c) 30 (d) 5
19. 19.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) 42 cm (b) 12 cm (c) 6 cm (d) 3 cm
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) 48 min (c) 140 min (d) 4 min
21. 21.What is the smallest number of sweets that can be shared equally among 6 children or among 8 children, with none left over? (a) 14 (b) 48 (c) 24 (d) 25
22. 22.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) 40 min (c) 18 min (d) 2 min
23. 23.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) 3 cm (c) 6 cm (d) 1 cm
24. 24.Two ribbons are 30 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) 5 cm (b) 10 cm (c) 40 cm (d) 30 cm
25. 25.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) 525 min (c) 50 min (d) 5 min
26. 26.Two bells ring every 18 minutes and every 42 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 126 min (b) 60 min (c) 6 min (d) 756 min
27. 27.What is the smallest number of sweets that can be shared equally among 12 children or among 14 children, with none left over? (a) 85 (b) 84 (c) 26 (d) 168
28. 28.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) 192 (c) 28 (d) 96
29. 29.Two ribbons are 60 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) 12 cm (c) 60 cm (d) 24 cm
30. 30.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) 2 min (b) 30 min (c) 16 min (d) 60 min
31. 31.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) 112 min (b) 22 min (c) 2 min (d) 56 min
32. 32.A teacher has 10 pencils and 15 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 30 (b) 10 (c) 1 (d) 5
33. 33.What is the smallest number of sweets that can be shared equally among 8 children or among 28 children, with none left over? (a) 36 (b) 224 (c) 112 (d) 56
34. 34.What is the smallest number of sweets that can be shared equally among 8 children or among 10 children, with none left over? (a) 18 (b) 41 (c) 80 (d) 40
35. 35.A teacher has 44 pencils and 55 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 11 (c) 44 (d) 220
36. 36.Two bells ring every 18 minutes and every 24 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 42 min (b) 432 min (c) 6 min (d) 72 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) 36 (b) 15 (c) 18 (d) 54
38. 38.Two bells ring every 18 minutes and every 30 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 90 min (b) 6 min (c) 540 min (d) 48 min
39. 39.A teacher has 32 pencils and 40 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 160 (b) 4 (c) 32 (d) 8
40. 40.A teacher has 12 pencils and 20 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 8 (b) 12 (c) 4 (d) 2

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