HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 295 · 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 25 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) 25 cm (b) 5 cm (c) 1 cm (d) 150 cm
2. 2.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) 2 min (b) 20 min (c) 14 min (d) 40 min
3. 3.Two ribbons are 9 cm and 21 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) 1 cm (c) 9 cm (d) 3 cm
4. 4.Two ribbons are 24 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) 72 cm (b) 24 cm (c) 12 cm (d) 6 cm
5. 5.Two bells ring every 20 minutes and every 25 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 500 min (b) 100 min (c) 45 min (d) 5 min
6. 6.A teacher has 20 pencils and 28 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 20 (b) 2 (c) 4 (d) 8
7. 7.What is the smallest number of sweets that can be shared equally among 6 children or among 15 children, with none left over? (a) 21 (b) 90 (c) 30 (d) 60
8. 8.A teacher has 20 pencils and 30 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 10 (b) 5 (c) 20 (d) 60
9. 9.Two bells ring every 15 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 105 min (b) 315 min (c) 36 min (d) 3 min
10. 10.A teacher has 6 pencils and 9 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 1 (c) 18 (d) 3
11. 11.Two ribbons are 12 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) 12 cm (b) 2 cm (c) 8 cm (d) 4 cm
12. 12.A teacher has 21 pencils and 56 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 35 (b) 21 (c) 7 (d) 1
13. 13.Two ribbons are 72 cm and 81 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 648 cm (b) 72 cm (c) 9 cm (d) 3 cm
14. 14.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) 40 min (b) 84 min (c) 336 min (d) 4 min
15. 15.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) 48 min (b) 6 min (c) 90 min (d) 540 min
16. 16.A teacher has 35 pencils and 56 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 7 (b) 21 (c) 35 (d) 1
17. 17.Two ribbons are 9 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) 9 cm (c) 3 cm (d) 36 cm
18. 18.Two bells ring every 20 minutes and every 35 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 700 min (b) 140 min (c) 55 min (d) 5 min
19. 19.What is the smallest number of sweets that can be shared equally among 18 children or among 24 children, with none left over? (a) 432 (b) 144 (c) 42 (d) 72
20. 20.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) 378 (c) 252 (d) 39
21. 21.A teacher has 30 pencils and 80 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 10 (b) 50 (c) 5 (d) 30
22. 22.Two ribbons are 40 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) 40 cm (b) 5 cm (c) 200 cm (d) 10 cm
23. 23.What is the smallest number of sweets that can be shared equally among 8 children or among 12 children, with none left over? (a) 48 (b) 24 (c) 96 (d) 20
24. 24.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) 41 (c) 18 (d) 80
25. 25.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) 28 min (b) 4 min (c) 48 min (d) 192 min
26. 26.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) 4 min (b) 96 min (c) 20 min (d) 24 min
27. 27.Two ribbons are 12 cm and 18 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) 6 cm (c) 12 cm (d) 3 cm
28. 28.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) 6 cm (b) 12 cm (c) 30 cm (d) 3 cm
29. 29.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) 180 min (b) 60 min (c) 27 min (d) 3 min
30. 30.A teacher has 14 pencils and 35 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 21 (b) 7 (c) 1 (d) 14
31. 31.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) 42 min (b) 20 min (c) 2 min (d) 84 min
32. 32.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) 15 (b) 12 (c) 1 (d) 3
33. 33.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) 2 min (b) 18 min (c) 28 min (d) 56 min
34. 34.What is the smallest number of sweets that can be shared equally among 9 children or among 15 children, with none left over? (a) 90 (b) 45 (c) 135 (d) 24
35. 35.A teacher has 8 pencils and 18 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 10 (b) 8 (c) 2 (d) 1
36. 36.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) 60 min (b) 2 min (c) 16 min (d) 30 min
37. 37.A teacher has 77 pencils and 99 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 22 (c) 11 (d) 77
38. 38.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) 2 min (b) 14 min (c) 24 min (d) 48 min
39. 39.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) 18 min (b) 40 min (c) 2 min (d) 80 min
40. 40.What is the smallest number of sweets that can be shared equally among 18 children or among 30 children, with none left over? (a) 540 (b) 90 (c) 180 (d) 48

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