HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 815 · 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.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) 60 min (b) 32 min (c) 240 min (d) 4 min
2. 2.What is the smallest number of sweets that can be shared equally among 10 children or among 14 children, with none left over? (a) 24 (b) 140 (c) 70 (d) 71
3. 3.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) 6 min (b) 60 min (c) 756 min (d) 126 min
4. 4.A teacher has 24 pencils and 42 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 6 (c) 24 (d) 18
5. 5.What is the smallest number of sweets that can be shared equally among 18 children or among 21 children, with none left over? (a) 126 (b) 252 (c) 39 (d) 378
6. 6.A teacher has 24 pencils and 84 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 60 (b) 12 (c) 24 (d) 6
7. 7.What is the smallest number of sweets that can be shared equally among 15 children or among 25 children, with none left over? (a) 40 (b) 375 (c) 150 (d) 75
8. 8.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
9. 9.What is the smallest number of sweets that can be shared equally among 20 children or among 28 children, with none left over? (a) 48 (b) 140 (c) 280 (d) 560
10. 10.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
11. 11.Two bells ring every 20 minutes and every 24 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 4 min (b) 120 min (c) 480 min (d) 44 min
12. 12.Two ribbons are 30 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) 20 cm (b) 5 cm (c) 30 cm (d) 10 cm
13. 13.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) 4 min (c) 336 min (d) 40 min
14. 14.What is the smallest number of sweets that can be shared equally among 25 children or among 30 children, with none left over? (a) 55 (b) 750 (c) 150 (d) 300
15. 15.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) 504 (c) 168 (d) 54
16. 16.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) 2 min (b) 12 min (c) 24 min (d) 10 min
17. 17.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
18. 18.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) 54 (d) 18
19. 19.What is the smallest number of sweets that can be shared equally among 6 children or among 8 children, with none left over? (a) 48 (b) 14 (c) 25 (d) 24
20. 20.Two bells ring every 10 minutes and every 12 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 120 min (b) 2 min (c) 60 min (d) 22 min
21. 21.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) 4 min (c) 80 min (d) 320 min
22. 22.A teacher has 15 pencils and 27 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) 12 (d) 3
23. 23.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
24. 24.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) 20 cm (b) 5 cm (c) 50 cm (d) 10 cm
25. 25.What is the smallest number of sweets that can be shared equally among 15 children or among 20 children, with none left over? (a) 35 (b) 120 (c) 300 (d) 60
26. 26.Two ribbons are 28 cm and 36 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) 8 cm (c) 4 cm (d) 28 cm
27. 27.Two ribbons are 35 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) 7 cm (b) 35 cm (c) 21 cm (d) 1 cm
28. 28.Two ribbons are 22 cm and 33 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 66 cm (b) 11 cm (c) 22 cm (d) 1 cm
29. 29.Two ribbons are 6 cm and 14 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) 6 cm (c) 2 cm (d) 8 cm
30. 30.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) 192 (c) 28 (d) 48
31. 31.Two ribbons are 16 cm and 20 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) 2 cm (d) 80 cm
32. 32.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) 84 min (b) 252 min (c) 33 min (d) 3 min
33. 33.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
34. 34.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
35. 35.A teacher has 42 pencils and 48 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 336 (c) 3 (d) 42
36. 36.A teacher has 8 pencils and 20 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 12 (b) 4 (c) 2 (d) 8
37. 37.A teacher has 10 pencils and 25 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 10 (b) 15 (c) 5 (d) 1
38. 38.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
39. 39.Two ribbons are 6 cm and 15 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) 3 cm (c) 6 cm (d) 1 cm
40. 40.Two ribbons are 12 cm and 16 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 48 cm (b) 2 cm (c) 12 cm (d) 4 cm

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