HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 149 · 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 30 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) 30 cm (b) 180 cm (c) 6 cm (d) 3 cm
2. 2.A teacher has 14 pencils and 49 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 35 (b) 1 (c) 7 (d) 14
3. 3.A teacher has 44 pencils and 77 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 11 (b) 44 (c) 33 (d) 1
4. 4.Two ribbons are 20 cm and 28 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 8 cm (b) 4 cm (c) 2 cm (d) 20 cm
5. 5.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) 14 min (b) 2 min (c) 20 min (d) 40 min
6. 6.Two ribbons are 60 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) 420 cm (b) 60 cm (c) 5 cm (d) 10 cm
7. 7.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) 36 min (c) 56 min (d) 224 min
8. 8.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) 24 min (c) 96 min (d) 20 min
9. 9.Two ribbons are 12 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
10. 10.Two ribbons are 84 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) 84 cm (b) 6 cm (c) 672 cm (d) 12 cm
11. 11.What is the smallest number of sweets that can be shared equally among 6 children or among 14 children, with none left over? (a) 42 (b) 84 (c) 43 (d) 20
12. 12.Two bells ring every 25 minutes and every 30 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 5 min (b) 150 min (c) 750 min (d) 55 min
13. 13.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) 36 cm (b) 3 cm (c) 1 cm (d) 9 cm
14. 14.A teacher has 20 pencils and 32 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 20 (b) 12 (c) 4 (d) 2
15. 15.Two ribbons are 10 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) 10 cm (b) 1 cm (c) 2 cm (d) 60 cm
16. 16.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) 315 min (b) 3 min (c) 36 min (d) 105 min
17. 17.Two ribbons are 55 cm and 99 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 44 cm (b) 55 cm (c) 11 cm (d) 1 cm
18. 18.A teacher has 24 pencils and 30 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 24 (b) 120 (c) 3 (d) 6
19. 19.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) 112 min (b) 56 min (c) 22 min (d) 2 min
20. 20.What is the smallest number of sweets that can be shared equally among 8 children or among 14 children, with none left over? (a) 56 (b) 22 (c) 112 (d) 57
21. 21.What is the smallest number of sweets that can be shared equally among 20 children or among 28 children, with none left over? (a) 560 (b) 48 (c) 280 (d) 140
22. 22.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) 168 min (b) 26 min (c) 2 min (d) 84 min
23. 23.What is the smallest number of sweets that can be shared equally among 20 children or among 25 children, with none left over? (a) 45 (b) 200 (c) 100 (d) 500
24. 24.Two ribbons are 30 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) 3 cm (b) 12 cm (c) 30 cm (d) 6 cm
25. 25.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) 24 (d) 90
26. 26.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) 44 min (c) 112 min (d) 448 min
27. 27.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) 4 min (b) 160 min (c) 40 min (d) 28 min
28. 28.Two ribbons are 20 cm and 32 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) 20 cm (c) 4 cm (d) 2 cm
29. 29.Two ribbons are 15 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) 1 cm (b) 6 cm (c) 15 cm (d) 3 cm
30. 30.Two ribbons are 40 cm and 64 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 8 cm (b) 4 cm (c) 24 cm (d) 40 cm
31. 31.What is the smallest number of sweets that can be shared equally among 20 children or among 24 children, with none left over? (a) 240 (b) 44 (c) 480 (d) 120
32. 32.A teacher has 8 pencils and 36 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 4 (b) 8 (c) 2 (d) 28
33. 33.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) 135 min (b) 24 min (c) 3 min (d) 45 min
34. 34.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) 150 min (b) 30 min (c) 25 min (d) 5 min
35. 35.Two ribbons are 36 cm and 60 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) 36 cm (c) 6 cm (d) 24 cm
36. 36.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) 25 (c) 24 (d) 14
37. 37.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) 33 min (c) 252 min (d) 3 min
38. 38.Two ribbons are 8 cm and 28 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) 8 cm (c) 4 cm (d) 2 cm
39. 39.A teacher has 8 pencils and 12 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 4 (b) 8 (c) 2 (d) 24
40. 40.What is the smallest number of sweets that can be shared equally among 24 children or among 30 children, with none left over? (a) 240 (b) 54 (c) 720 (d) 120

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