HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 767 · 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 24 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) 24 cm (b) 96 cm (c) 8 cm (d) 4 cm
2. 2.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
3. 3.A teacher has 20 pencils and 35 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 20 (c) 5 (d) 15
4. 4.A teacher has 6 pencils and 16 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 2 (b) 6 (c) 1 (d) 10
5. 5.A teacher has 30 pencils and 35 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 30 (c) 210 (d) 5
6. 6.A teacher has 10 pencils and 45 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 10 (b) 35 (c) 5 (d) 1
7. 7.Two ribbons are 16 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) 1 cm (b) 144 cm (c) 16 cm (d) 2 cm
8. 8.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) 11 cm (c) 330 cm (d) 55 cm
9. 9.Two ribbons are 24 cm and 27 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) 216 cm (d) 1 cm
10. 10.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) 126 min (b) 3 min (c) 27 min (d) 42 min
11. 11.What is the smallest number of sweets that can be shared equally among 16 children or among 28 children, with none left over? (a) 224 (b) 112 (c) 44 (d) 448
12. 12.What is the smallest number of sweets that can be shared equally among 9 children or among 15 children, with none left over? (a) 24 (b) 135 (c) 45 (d) 90
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) 1 cm (b) 3 cm (c) 9 cm (d) 36 cm
14. 14.A teacher has 6 pencils and 15 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 6 (c) 9 (d) 3
15. 15.What is the smallest number of sweets that can be shared equally among 10 children or among 35 children, with none left over? (a) 140 (b) 45 (c) 70 (d) 350
16. 16.Two ribbons are 21 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) 21 cm (b) 28 cm (c) 1 cm (d) 7 cm
17. 17.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) 84 min (c) 6 min (d) 54 min
18. 18.A teacher has 16 pencils and 28 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 16 (b) 4 (c) 2 (d) 12
19. 19.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) 18 min (c) 54 min (d) 3 min
20. 20.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) 36 min (b) 105 min (c) 3 min (d) 315 min
21. 21.Two ribbons are 24 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) 36 cm (b) 6 cm (c) 24 cm (d) 12 cm
22. 22.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) 525 min (b) 5 min (c) 105 min (d) 50 min
23. 23.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) 5 cm (b) 10 cm (c) 1 cm (d) 35 cm
24. 24.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) 36 cm (b) 12 cm (c) 24 cm (d) 6 cm
25. 25.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) 20 min (b) 42 min (c) 84 min (d) 2 min
26. 26.A teacher has 88 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) 792 (c) 88 (d) 11
27. 27.What is the smallest number of sweets that can be shared equally among 8 children or among 28 children, with none left over? (a) 224 (b) 56 (c) 112 (d) 36
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) 1 cm (b) 49 cm (c) 7 cm (d) 392 cm
29. 29.Two ribbons are 28 cm and 63 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) 28 cm (c) 35 cm (d) 7 cm
30. 30.Two ribbons are 30 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) 24 cm (b) 3 cm (c) 30 cm (d) 6 cm
31. 31.Two ribbons are 33 cm and 55 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) 22 cm (c) 11 cm (d) 33 cm
32. 32.Two bells ring every 20 minutes and every 28 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 140 min (b) 48 min (c) 560 min (d) 4 min
33. 33.Two bells ring every 15 minutes and every 20 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 35 min (b) 300 min (c) 60 min (d) 5 min
34. 34.A teacher has 24 pencils and 27 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 24 (b) 3 (c) 216 (d) 1
35. 35.A teacher has 49 pencils and 63 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 14 (b) 1 (c) 7 (d) 49
36. 36.Two ribbons are 63 cm and 72 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) 504 cm (c) 9 cm (d) 63 cm
37. 37.Two ribbons are 60 cm and 72 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 360 cm (b) 6 cm (c) 12 cm (d) 60 cm
38. 38.Two ribbons are 18 cm and 27 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 54 cm (b) 18 cm (c) 9 cm (d) 3 cm
39. 39.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) 55 min (c) 750 min (d) 150 min
40. 40.Two bells ring every 10 minutes and every 35 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 70 min (b) 45 min (c) 5 min (d) 350 min

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