HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 409 · 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) 56 (c) 22 (d) 112
2. 2.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) 189 min (b) 3 min (c) 30 min (d) 63 min
3. 3.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) 336 (b) 42 (c) 6 (d) 3
4. 4.A teacher has 55 pencils and 66 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 330 (b) 11 (c) 1 (d) 55
5. 5.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) 30 min (b) 216 min (c) 6 min (d) 36 min
6. 6.Two ribbons are 55 cm and 66 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) 330 cm (c) 11 cm (d) 55 cm
7. 7.A teacher has 4 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) 2 (c) 4 (d) 14
8. 8.What is the smallest number of sweets that can be shared equally among 4 children or among 6 children, with none left over? (a) 13 (b) 24 (c) 10 (d) 12
9. 9.Two bells ring every 15 minutes and every 18 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 90 min (b) 3 min (c) 270 min (d) 33 min
10. 10.Two ribbons are 48 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) 4 cm (b) 336 cm (c) 8 cm (d) 48 cm
11. 11.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) 15 (c) 18 (d) 36
12. 12.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) 504 min (b) 6 min (c) 54 min (d) 84 min
13. 13.Two ribbons are 18 cm and 48 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) 30 cm (c) 18 cm (d) 3 cm
14. 14.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) 6 min (c) 432 min (d) 72 min
15. 15.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) 44 min (b) 120 min (c) 4 min (d) 480 min
16. 16.Two ribbons are 10 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) 10 cm (b) 35 cm (c) 1 cm (d) 5 cm
17. 17.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
18. 18.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) 32 min (b) 4 min (c) 60 min (d) 240 min
19. 19.A teacher has 9 pencils and 15 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 9 (b) 1 (c) 3 (d) 6
20. 20.A teacher has 18 pencils and 24 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 18 (c) 72 (d) 3
21. 21.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) 540 min (b) 48 min (c) 90 min (d) 6 min
22. 22.What is the smallest number of sweets that can be shared equally among 12 children or among 28 children, with none left over? (a) 84 (b) 40 (c) 168 (d) 336
23. 23.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) 3 min (c) 42 min (d) 126 min
24. 24.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
25. 25.Two ribbons are 48 cm and 108 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 60 cm (b) 48 cm (c) 12 cm (d) 6 cm
26. 26.Two bells ring every 12 minutes and every 15 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 3 min (b) 27 min (c) 180 min (d) 60 min
27. 27.A teacher has 12 pencils and 28 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) 12 (d) 16
28. 28.Two bells ring every 16 minutes and every 28 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 4 min (b) 112 min (c) 44 min (d) 448 min
29. 29.A teacher has 4 pencils and 6 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 12 (b) 2 (c) 1 (d) 4
30. 30.What is the smallest number of sweets that can be shared equally among 12 children or among 14 children, with none left over? (a) 26 (b) 85 (c) 168 (d) 84
31. 31.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) 96 min (b) 20 min (c) 24 min (d) 4 min
32. 32.Two ribbons are 24 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) 24 cm (b) 18 cm (c) 6 cm (d) 3 cm
33. 33.A teacher has 12 pencils and 18 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 12 (b) 3 (c) 6 (d) 36
34. 34.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) 1 cm (b) 9 cm (c) 3 cm (d) 6 cm
35. 35.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) 56 min (c) 36 min (d) 224 min
36. 36.A teacher has 40 pencils and 90 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 10 (b) 40 (c) 5 (d) 50
37. 37.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) 120 min (b) 54 min (c) 720 min (d) 6 min
38. 38.Two ribbons are 35 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) 210 cm (b) 1 cm (c) 35 cm (d) 7 cm
39. 39.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) 12 min (b) 2 min (c) 24 min (d) 10 min
40. 40.Two bells ring every 12 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 2 min (b) 168 min (c) 26 min (d) 84 min

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