HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 468 · 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 ribbons are 6 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) 6 cm (b) 10 cm (c) 1 cm (d) 2 cm
2. 2.Two ribbons are 24 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) 24 cm (b) 12 cm (c) 6 cm (d) 60 cm
3. 3.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
4. 4.What is the smallest number of sweets that can be shared equally among 4 children or among 6 children, with none left over? (a) 12 (b) 10 (c) 24 (d) 13
5. 5.What is the smallest number of sweets that can be shared equally among 16 children or among 20 children, with none left over? (a) 36 (b) 160 (c) 320 (d) 80
6. 6.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) 1 (b) 4 (c) 12 (d) 2
7. 7.Two ribbons are 60 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) 60 cm (b) 12 cm (c) 36 cm (d) 6 cm
8. 8.What is the smallest number of sweets that can be shared equally among 8 children or among 10 children, with none left over? (a) 80 (b) 18 (c) 41 (d) 40
9. 9.Two ribbons are 14 cm and 49 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 14 cm (b) 1 cm (c) 35 cm (d) 7 cm
10. 10.Two bells ring every 4 minutes and every 10 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 40 min (b) 14 min (c) 2 min (d) 20 min
11. 11.A teacher has 24 pencils and 28 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 168 (b) 24 (c) 4 (d) 2
12. 12.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) 5 min (b) 25 min (c) 150 min (d) 30 min
13. 13.Two ribbons are 8 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) 8 cm (c) 6 cm (d) 2 cm
14. 14.What is the smallest number of sweets that can be shared equally among 9 children or among 15 children, with none left over? (a) 45 (b) 135 (c) 90 (d) 24
15. 15.Two ribbons are 24 cm and 30 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) 3 cm (c) 120 cm (d) 6 cm
16. 16.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) 1 (b) 55 (c) 11 (d) 330
17. 17.What is the smallest number of sweets that can be shared equally among 20 children or among 35 children, with none left over? (a) 280 (b) 55 (c) 140 (d) 700
18. 18.Two bells ring every 6 minutes and every 8 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 48 min (b) 14 min (c) 24 min (d) 2 min
19. 19.A teacher has 12 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
20. 20.Two bells ring every 9 minutes and every 12 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 108 min (b) 3 min (c) 36 min (d) 21 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) 54 min (b) 15 min (c) 3 min (d) 18 min
22. 22.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) 72 min (b) 432 min (c) 42 min (d) 6 min
23. 23.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) 3 min (b) 63 min (c) 30 min (d) 189 min
24. 24.Two ribbons are 42 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) 6 cm (b) 12 cm (c) 42 cm (d) 3 cm
25. 25.What is the smallest number of sweets that can be shared equally among 10 children or among 35 children, with none left over? (a) 70 (b) 350 (c) 45 (d) 140
26. 26.What is the smallest number of sweets that can be shared equally among 18 children or among 24 children, with none left over? (a) 144 (b) 42 (c) 72 (d) 432
27. 27.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) 48 min (b) 28 min (c) 192 min (d) 4 min
28. 28.Two ribbons are 49 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) 49 cm (b) 1 cm (c) 7 cm (d) 392 cm
29. 29.What is the smallest number of sweets that can be shared equally among 12 children or among 15 children, with none left over? (a) 120 (b) 60 (c) 180 (d) 27
30. 30.A teacher has 20 pencils and 24 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 120 (b) 2 (c) 20 (d) 4
31. 31.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) 36 min (c) 6 min (d) 216 min
32. 32.Two ribbons are 40 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) 40 cm (c) 8 cm (d) 16 cm
33. 33.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) 5 min (c) 105 min (d) 525 min
34. 34.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) 75 min (b) 375 min (c) 40 min (d) 5 min
35. 35.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) 22 cm (c) 1 cm (d) 11 cm
36. 36.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) 300 (c) 60 (d) 120
37. 37.A teacher has 16 pencils and 24 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 48 (b) 8 (c) 16 (d) 4
38. 38.A teacher has 36 pencils and 84 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 36 (b) 48 (c) 6 (d) 12
39. 39.Two bells ring every 12 minutes and every 30 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 42 min (b) 60 min (c) 6 min (d) 360 min
40. 40.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) 24 min (b) 4 min (c) 96 min (d) 20 min

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