HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 947 · 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.A teacher has 35 pencils and 40 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) 5 (d) 280
2. 2.A teacher has 9 pencils and 15 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) 9 (d) 1
3. 3.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) 54 min (b) 84 min (c) 504 min (d) 6 min
4. 4.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
5. 5.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) 2 min (c) 26 min (d) 84 min
6. 6.Two ribbons are 14 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) 14 cm (b) 1 cm (c) 7 cm (d) 21 cm
7. 7.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) 3 min (b) 45 min (c) 24 min (d) 135 min
8. 8.Two ribbons are 96 cm and 108 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) 864 cm (c) 12 cm (d) 96 cm
9. 9.A teacher has 45 pencils and 81 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 36 (b) 45 (c) 9 (d) 3
10. 10.What is the smallest number of sweets that can be shared equally among 25 children or among 30 children, with none left over? (a) 750 (b) 300 (c) 150 (d) 55
11. 11.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) 8 cm (b) 2 cm (c) 1 cm (d) 6 cm
12. 12.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
13. 13.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) 24 min (b) 12 min (c) 10 min (d) 2 min
14. 14.What is the smallest number of sweets that can be shared equally among 20 children or among 35 children, with none left over? (a) 55 (b) 140 (c) 280 (d) 700
15. 15.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) 5 min (b) 50 min (c) 525 min (d) 105 min
16. 16.A teacher has 24 pencils and 84 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 24 (b) 12 (c) 6 (d) 60
17. 17.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) 16 cm (c) 144 cm (d) 2 cm
18. 18.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) 36 (c) 112 (d) 56
19. 19.What is the smallest number of sweets that can be shared equally among 8 children or among 12 children, with none left over? (a) 96 (b) 48 (c) 20 (d) 24
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) 22 (b) 56 (c) 57 (d) 112
21. 21.What is the smallest number of sweets that can be shared equally among 12 children or among 16 children, with none left over? (a) 96 (b) 48 (c) 192 (d) 28
22. 22.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) 36 min (b) 30 min (c) 6 min (d) 216 min
23. 23.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) 16 min (c) 30 min (d) 2 min
24. 24.Two ribbons are 12 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) 16 cm (b) 4 cm (c) 2 cm (d) 12 cm
25. 25.What is the smallest number of sweets that can be shared equally among 9 children or among 12 children, with none left over? (a) 36 (b) 108 (c) 72 (d) 21
26. 26.What is the smallest number of sweets that can be shared equally among 6 children or among 8 children, with none left over? (a) 25 (b) 14 (c) 48 (d) 24
27. 27.A teacher has 10 pencils and 16 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) 10 (d) 2
28. 28.Two ribbons are 4 cm and 10 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) 6 cm (c) 4 cm (d) 1 cm
29. 29.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) 84 min (b) 2 min (c) 20 min (d) 42 min
30. 30.A teacher has 15 pencils and 40 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 5 (c) 15 (d) 25
31. 31.Two ribbons are 40 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) 50 cm (c) 10 cm (d) 40 cm
32. 32.Two bells ring every 16 minutes and every 20 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 320 min (b) 80 min (c) 36 min (d) 4 min
33. 33.A teacher has 24 pencils and 42 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 18 (c) 6 (d) 24
34. 34.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) 126 min (c) 756 min (d) 60 min
35. 35.Two ribbons are 24 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) 24 cm (b) 8 cm (c) 4 cm (d) 32 cm
36. 36.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) 1 cm (b) 24 cm (c) 216 cm (d) 3 cm
37. 37.Two ribbons are 14 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) 7 cm (c) 14 cm (d) 42 cm
38. 38.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) 4 cm (b) 8 cm (c) 96 cm (d) 24 cm
39. 39.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) 9 (b) 1 (c) 6 (d) 3
40. 40.Two bells ring every 12 minutes and every 30 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 360 min (b) 60 min (c) 6 min (d) 42 min

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