HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 175 · 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 8 children or among 14 children, with none left over? (a) 57 (b) 112 (c) 22 (d) 56
2. 2.What is the smallest number of sweets that can be shared equally among 6 children or among 10 children, with none left over? (a) 60 (b) 16 (c) 31 (d) 30
3. 3.What is the smallest number of sweets that can be shared equally among 12 children or among 16 children, with none left over? (a) 96 (b) 48 (c) 28 (d) 192
4. 4.Two ribbons are 15 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) 15 cm (c) 12 cm (d) 1 cm
5. 5.What is the smallest number of sweets that can be shared equally among 16 children or among 28 children, with none left over? (a) 112 (b) 224 (c) 448 (d) 44
6. 6.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) 3 min (b) 378 min (c) 39 min (d) 126 min
7. 7.What is the smallest number of sweets that can be shared equally among 9 children or among 12 children, with none left over? (a) 108 (b) 72 (c) 36 (d) 21
8. 8.Two ribbons are 66 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) 66 cm (c) 1 cm (d) 462 cm
9. 9.A teacher has 15 pencils and 24 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 15 (c) 3 (d) 9
10. 10.Two bells ring every 8 minutes and every 20 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 28 min (b) 40 min (c) 160 min (d) 4 min
11. 11.What is the smallest number of sweets that can be shared equally among 12 children or among 28 children, with none left over? (a) 168 (b) 40 (c) 84 (d) 336
12. 12.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) 48 (c) 180 (d) 540
13. 13.A teacher has 18 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) 9 (c) 27 (d) 18
14. 14.Two ribbons are 12 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) 12 cm (b) 30 cm (c) 6 cm (d) 3 cm
15. 15.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) 33 cm (b) 22 cm (c) 1 cm (d) 11 cm
16. 16.What is the smallest number of sweets that can be shared equally among 12 children or among 18 children, with none left over? (a) 36 (b) 216 (c) 30 (d) 72
17. 17.What is the smallest number of sweets that can be shared equally among 8 children or among 10 children, with none left over? (a) 40 (b) 18 (c) 41 (d) 80
18. 18.What is the smallest number of sweets that can be shared equally among 25 children or among 30 children, with none left over? (a) 150 (b) 300 (c) 750 (d) 55
19. 19.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) 21 min (c) 3 min (d) 90 min
20. 20.Two ribbons are 36 cm and 96 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 36 cm (b) 12 cm (c) 6 cm (d) 60 cm
21. 21.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) 3 min (b) 45 min (c) 135 min (d) 24 min
22. 22.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) 25 min (b) 5 min (c) 30 min (d) 150 min
23. 23.A teacher has 40 pencils and 45 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 360 (b) 40 (c) 5 (d) 1
24. 24.Two ribbons are 77 cm and 88 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 77 cm (b) 1 cm (c) 616 cm (d) 11 cm
25. 25.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) 40 min (d) 84 min
26. 26.Two ribbons are 8 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) 1 cm (b) 40 cm (c) 2 cm (d) 8 cm
27. 27.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) 60 (c) 30 (d) 150
28. 28.Two ribbons are 33 cm and 44 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) 132 cm (c) 11 cm (d) 33 cm
29. 29.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) 432 min (b) 42 min (c) 6 min (d) 72 min
30. 30.A teacher has 44 pencils and 99 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 55 (b) 1 (c) 11 (d) 44
31. 31.A teacher has 35 pencils and 40 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 35 (b) 280 (c) 1 (d) 5
32. 32.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) 2 min (c) 24 min (d) 12 min
33. 33.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) 375 min (b) 40 min (c) 75 min (d) 5 min
34. 34.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) 56 min (b) 22 min (c) 2 min (d) 112 min
35. 35.Two bells ring every 12 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 3 min (b) 252 min (c) 33 min (d) 84 min
36. 36.Two ribbons are 16 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) 56 cm (b) 8 cm (c) 16 cm (d) 4 cm
37. 37.Two ribbons are 35 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) 35 cm (b) 1 cm (c) 10 cm (d) 5 cm
38. 38.A teacher has 12 pencils and 54 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 12 (b) 6 (c) 3 (d) 42
39. 39.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) 50 min (b) 525 min (c) 5 min (d) 105 min
40. 40.A teacher has 20 pencils and 90 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 70 (b) 10 (c) 5 (d) 20

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