HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 371 · 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 8 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) 2 cm (b) 28 cm (c) 4 cm (d) 8 cm
2. 2.A teacher has 36 pencils and 48 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 144 (c) 36 (d) 12
3. 3.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) 5 min (c) 375 min (d) 40 min
4. 4.Two ribbons are 8 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) 2 cm (b) 8 cm (c) 4 cm (d) 24 cm
5. 5.A teacher has 24 pencils and 108 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 12 (b) 84 (c) 6 (d) 24
6. 6.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) 2 (b) 6 (c) 8 (d) 1
7. 7.What is the smallest number of sweets that can be shared equally among 18 children or among 42 children, with none left over? (a) 252 (b) 756 (c) 126 (d) 60
8. 8.What is the smallest number of sweets that can be shared equally among 20 children or among 35 children, with none left over? (a) 700 (b) 55 (c) 140 (d) 280
9. 9.What is the smallest number of sweets that can be shared equally among 6 children or among 8 children, with none left over? (a) 14 (b) 25 (c) 48 (d) 24
10. 10.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) 14 min (b) 48 min (c) 24 min (d) 2 min
11. 11.Two ribbons are 45 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) 27 cm (b) 45 cm (c) 3 cm (d) 9 cm
12. 12.A teacher has 50 pencils and 80 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 50 (b) 10 (c) 30 (d) 5
13. 13.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) 2 min (b) 30 min (c) 16 min (d) 60 min
14. 14.A teacher has 14 pencils and 21 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 14 (c) 7 (d) 42
15. 15.What is the smallest number of sweets that can be shared equally among 15 children or among 25 children, with none left over? (a) 375 (b) 40 (c) 75 (d) 150
16. 16.Two bells ring every 10 minutes and every 25 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 250 min (b) 5 min (c) 50 min (d) 35 min
17. 17.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
18. 18.Two bells ring every 4 minutes and every 6 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 10 min (b) 2 min (c) 24 min (d) 12 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) 42 (b) 144 (c) 72 (d) 432
20. 20.Two ribbons are 12 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) 9 cm (c) 12 cm (d) 3 cm
21. 21.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) 315 min (c) 3 min (d) 105 min
22. 22.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) 24 cm (b) 40 cm (c) 8 cm (d) 4 cm
23. 23.A teacher has 42 pencils and 54 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 42 (c) 12 (d) 6
24. 24.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) 9 (b) 3 (c) 648 (d) 72
25. 25.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) 24 min (b) 135 min (c) 3 min (d) 45 min
26. 26.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) 3 (b) 12 (c) 1 (d) 15
27. 27.A teacher has 4 pencils and 18 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 2 (b) 4 (c) 14 (d) 1
28. 28.A teacher has 18 pencils and 45 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 9 (b) 27 (c) 3 (d) 18
29. 29.What is the smallest number of sweets that can be shared equally among 12 children or among 28 children, with none left over? (a) 40 (b) 84 (c) 168 (d) 336
30. 30.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) 28 min (b) 56 min (c) 2 min (d) 18 min
31. 31.Two ribbons are 48 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) 48 cm (b) 8 cm (c) 336 cm (d) 4 cm
32. 32.Two ribbons are 6 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
33. 33.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) 84 min (c) 20 min (d) 2 min
34. 34.Two ribbons are 20 cm and 90 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) 70 cm (d) 20 cm
35. 35.A teacher has 12 pencils and 16 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 12 (b) 48 (c) 2 (d) 4
36. 36.Two ribbons are 50 cm and 80 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) 5 cm (c) 30 cm (d) 50 cm
37. 37.A teacher has 32 pencils and 72 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 40 (b) 32 (c) 8 (d) 4
38. 38.What is the smallest number of sweets that can be shared equally among 12 children or among 30 children, with none left over? (a) 360 (b) 60 (c) 120 (d) 42
39. 39.Two ribbons are 22 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) 11 cm (b) 1 cm (c) 33 cm (d) 22 cm
40. 40.Two ribbons are 25 cm and 35 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) 25 cm (c) 5 cm (d) 1 cm

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