HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 807 · 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 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) 22 min (c) 2 min (d) 56 min
2. 2.A teacher has 15 pencils and 18 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 15 (b) 90 (c) 3 (d) 1
3. 3.Two ribbons are 6 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) 6 cm (b) 1 cm (c) 4 cm (d) 2 cm
4. 4.What is the smallest number of sweets that can be shared equally among 4 children or among 14 children, with none left over? (a) 56 (b) 28 (c) 29 (d) 18
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) 2 min (b) 40 min (c) 20 min (d) 14 min
6. 6.What is the smallest number of sweets that can be shared equally among 6 children or among 21 children, with none left over? (a) 27 (b) 42 (c) 84 (d) 126
7. 7.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) 180 (c) 60 (d) 27
8. 8.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
9. 9.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) 42 min (d) 27 min
10. 10.Two ribbons are 40 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) 8 cm (b) 40 cm (c) 16 cm (d) 4 cm
11. 11.Two ribbons are 18 cm and 30 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) 6 cm (c) 12 cm (d) 3 cm
12. 12.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) 12 (b) 2 (c) 4 (d) 20
13. 13.A teacher has 45 pencils and 72 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 45 (b) 3 (c) 27 (d) 9
14. 14.What is the smallest number of sweets that can be shared equally among 15 children or among 25 children, with none left over? (a) 150 (b) 75 (c) 40 (d) 375
15. 15.Two ribbons are 4 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) 4 cm (b) 14 cm (c) 2 cm (d) 1 cm
16. 16.Two bells ring every 9 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 189 min (b) 3 min (c) 30 min (d) 63 min
17. 17.What is the smallest number of sweets that can be shared equally among 9 children or among 12 children, with none left over? (a) 72 (b) 36 (c) 108 (d) 21
18. 18.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) 20 (c) 84 (d) 42
19. 19.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) 5 (b) 280 (c) 1 (d) 35
20. 20.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) 4 min (b) 560 min (c) 140 min (d) 48 min
21. 21.Two ribbons are 12 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) 2 cm (b) 4 cm (c) 48 cm (d) 12 cm
22. 22.A teacher has 20 pencils and 36 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) 20 (d) 16
23. 23.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) 14 (b) 1 (c) 35 (d) 7
24. 24.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) 4 (b) 2 (c) 48 (d) 12
25. 25.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) 864 cm (b) 12 cm (c) 96 cm (d) 6 cm
26. 26.Two ribbons are 15 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) 1 cm (b) 5 cm (c) 15 cm (d) 20 cm
27. 27.Two ribbons are 14 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) 7 cm (b) 35 cm (c) 14 cm (d) 1 cm
28. 28.Two ribbons are 15 cm and 25 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 15 cm (b) 1 cm (c) 10 cm (d) 5 cm
29. 29.Two ribbons are 12 cm and 20 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) 12 cm (c) 2 cm (d) 4 cm
30. 30.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) 750 min (b) 5 min (c) 55 min (d) 150 min
31. 31.What is the smallest number of sweets that can be shared equally among 6 children or among 9 children, with none left over? (a) 36 (b) 54 (c) 15 (d) 18
32. 32.A teacher has 30 pencils and 54 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 24 (c) 3 (d) 30
33. 33.A teacher has 30 pencils and 40 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 10 (b) 5 (c) 120 (d) 30
34. 34.Two ribbons are 28 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) 8 cm (d) 4 cm
35. 35.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
36. 36.What is the smallest number of sweets that can be shared equally among 20 children or among 25 children, with none left over? (a) 200 (b) 45 (c) 500 (d) 100
37. 37.A teacher has 22 pencils and 99 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 22 (b) 11 (c) 1 (d) 77
38. 38.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) 105 min (c) 50 min (d) 525 min
39. 39.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) 6 cm (b) 24 cm (c) 36 cm (d) 12 cm
40. 40.Two bells ring every 9 minutes and every 12 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 3 min (b) 108 min (c) 21 min (d) 36 min

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