HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 349 · 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 60 cm and 96 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) 12 cm (d) 60 cm
2. 2.What is the smallest number of sweets that can be shared equally among 8 children or among 10 children, with none left over? (a) 40 (b) 41 (c) 80 (d) 18
3. 3.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) 77 (b) 11 (c) 1 (d) 22
4. 4.Two ribbons are 12 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) 2 cm (b) 20 cm (c) 4 cm (d) 12 cm
5. 5.What is the smallest number of sweets that can be shared equally among 8 children or among 14 children, with none left over? (a) 57 (b) 56 (c) 112 (d) 22
6. 6.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) 10 (d) 12
7. 7.Two bells ring every 10 minutes and every 15 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 30 min (b) 5 min (c) 25 min (d) 150 min
8. 8.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) 42 min (b) 6 min (c) 60 min (d) 360 min
9. 9.Two bells ring every 24 minutes and every 30 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 120 min (b) 6 min (c) 54 min (d) 720 min
10. 10.What is the smallest number of sweets that can be shared equally among 24 children or among 30 children, with none left over? (a) 54 (b) 720 (c) 240 (d) 120
11. 11.Two ribbons are 21 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) 6 cm (b) 1 cm (c) 3 cm (d) 21 cm
12. 12.A teacher has 9 pencils and 12 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 36 (c) 1 (d) 9
13. 13.A teacher has 96 pencils and 108 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 12 (c) 96 (d) 864
14. 14.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) 5 (b) 30 (c) 10 (d) 50
15. 15.What is the smallest number of sweets that can be shared equally among 10 children or among 12 children, with none left over? (a) 60 (b) 22 (c) 120 (d) 61
16. 16.Two ribbons are 15 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) 5 cm (b) 1 cm (c) 60 cm (d) 15 cm
17. 17.A teacher has 8 pencils and 36 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 28 (b) 4 (c) 2 (d) 8
18. 18.Two ribbons are 84 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) 24 cm (b) 12 cm (c) 6 cm (d) 84 cm
19. 19.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) 8 cm (b) 28 cm (c) 2 cm (d) 4 cm
20. 20.What is the smallest number of sweets that can be shared equally among 20 children or among 25 children, with none left over? (a) 500 (b) 100 (c) 45 (d) 200
21. 21.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) 50 min (b) 5 min (c) 105 min (d) 525 min
22. 22.Two bells ring every 8 minutes and every 12 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 24 min (b) 4 min (c) 20 min (d) 96 min
23. 23.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) 24 min (b) 2 min (c) 48 min (d) 14 min
24. 24.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
25. 25.What is the smallest number of sweets that can be shared equally among 6 children or among 10 children, with none left over? (a) 30 (b) 60 (c) 31 (d) 16
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) 48 (c) 14 (d) 24
27. 27.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) 21 min (b) 108 min (c) 36 min (d) 3 min
28. 28.What is the smallest number of sweets that can be shared equally among 15 children or among 18 children, with none left over? (a) 90 (b) 270 (c) 33 (d) 180
29. 29.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) 126 (d) 84
30. 30.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) 756 min (b) 60 min (c) 126 min (d) 6 min
31. 31.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) 1 (b) 9 (c) 3 (d) 12
32. 32.Two ribbons are 48 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) 48 cm (b) 12 cm (c) 6 cm (d) 60 cm
33. 33.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) 4 min (c) 44 min (d) 448 min
34. 34.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) 2 min (b) 12 min (c) 24 min (d) 10 min
35. 35.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) 2 cm (c) 1 cm (d) 14 cm
36. 36.Two ribbons are 30 cm and 48 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 30 cm (b) 18 cm (c) 3 cm (d) 6 cm
37. 37.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) 2 min (d) 84 min
38. 38.Two ribbons are 42 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) 6 cm (b) 42 cm (c) 3 cm (d) 12 cm
39. 39.Two ribbons are 56 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) 56 cm (b) 4 cm (c) 16 cm (d) 8 cm
40. 40.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) 12 (b) 6 (c) 144 (d) 36

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