HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 887 · 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 9 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 18 cm (b) 3 cm (c) 6 cm (d) 1 cm
2. 2.A teacher has 16 pencils and 20 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 16 (b) 80 (c) 4 (d) 2
3. 3.Two ribbons are 8 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) 2 cm (b) 8 cm (c) 1 cm (d) 10 cm
4. 4.What is the smallest number of sweets that can be shared equally among 15 children or among 35 children, with none left over? (a) 105 (b) 525 (c) 50 (d) 210
5. 5.A teacher has 72 pencils and 84 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 12 (b) 6 (c) 72 (d) 504
6. 6.What is the smallest number of sweets that can be shared equally among 12 children or among 18 children, with none left over? (a) 216 (b) 30 (c) 36 (d) 72
7. 7.A teacher has 12 pencils and 32 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 4 (b) 20 (c) 2 (d) 12
8. 8.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) 18 min (b) 54 min (c) 15 min (d) 3 min
9. 9.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) 112 min (b) 448 min (c) 44 min (d) 4 min
10. 10.What is the smallest number of sweets that can be shared equally among 12 children or among 15 children, with none left over? (a) 27 (b) 180 (c) 120 (d) 60
11. 11.Two ribbons are 32 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) 288 cm (b) 32 cm (c) 4 cm (d) 2 cm
12. 12.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) 2 min (b) 56 min (c) 112 min (d) 22 min
13. 13.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) 24 (c) 14 (d) 25
14. 14.Two ribbons are 56 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) 448 cm (b) 56 cm (c) 8 cm (d) 4 cm
15. 15.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) 6 min (b) 216 min (c) 30 min (d) 36 min
16. 16.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) 750 min (c) 150 min (d) 55 min
17. 17.What is the smallest number of sweets that can be shared equally among 18 children or among 30 children, with none left over? (a) 48 (b) 180 (c) 90 (d) 540
18. 18.A teacher has 72 pencils and 81 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 72 (b) 9 (c) 648 (d) 3
19. 19.What is the smallest number of sweets that can be shared equally among 15 children or among 21 children, with none left over? (a) 315 (b) 210 (c) 36 (d) 105
20. 20.A teacher has 40 pencils and 48 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) 240 (d) 40
21. 21.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) 56 min (b) 224 min (c) 4 min (d) 36 min
22. 22.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) 12 cm (c) 6 cm (d) 24 cm
23. 23.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
24. 24.A teacher has 6 pencils and 14 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) 8 (d) 2
25. 25.Two ribbons are 10 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) 10 cm (b) 1 cm (c) 6 cm (d) 2 cm
26. 26.What is the smallest number of sweets that can be shared equally among 6 children or among 14 children, with none left over? (a) 43 (b) 84 (c) 42 (d) 20
27. 27.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) 12 (d) 10
28. 28.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
29. 29.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) 3 (c) 72 (d) 18
30. 30.A teacher has 9 pencils and 21 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) 9 (d) 1
31. 31.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) 9 cm (b) 12 cm (c) 1 cm (d) 3 cm
32. 32.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) 16 min (b) 30 min (c) 2 min (d) 60 min
33. 33.Two ribbons are 16 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) 16 cm (b) 2 cm (c) 4 cm (d) 20 cm
34. 34.Two ribbons are 40 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) 40 cm (b) 4 cm (c) 8 cm (d) 32 cm
35. 35.Two bells ring every 18 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 39 min (b) 378 min (c) 3 min (d) 126 min
36. 36.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) 7 cm (d) 1 cm
37. 37.Two ribbons are 18 cm and 24 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 18 cm (b) 72 cm (c) 3 cm (d) 6 cm
38. 38.Two ribbons are 24 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) 30 cm (c) 6 cm (d) 3 cm
39. 39.Two bells ring every 18 minutes and every 42 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 6 min (b) 60 min (c) 756 min (d) 126 min
40. 40.Two ribbons are 22 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) 1 cm (b) 22 cm (c) 11 cm (d) 77 cm

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