HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 136 · 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 15 pencils and 35 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 20 (c) 15 (d) 5
2. 2.What is the smallest number of sweets that can be shared equally among 8 children or among 12 children, with none left over? (a) 20 (b) 48 (c) 96 (d) 24
3. 3.What is the smallest number of sweets that can be shared equally among 6 children or among 14 children, with none left over? (a) 20 (b) 42 (c) 84 (d) 43
4. 4.Two ribbons are 12 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) 6 cm (b) 3 cm (c) 18 cm (d) 12 cm
5. 5.A teacher has 40 pencils and 50 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 5 (b) 10 (c) 40 (d) 200
6. 6.Two ribbons are 60 cm and 70 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 420 cm (b) 60 cm (c) 10 cm (d) 5 cm
7. 7.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) 32 cm (b) 2 cm (c) 288 cm (d) 4 cm
8. 8.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) 2 min (c) 30 min (d) 60 min
9. 9.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) 3 cm (c) 24 cm (d) 216 cm
10. 10.Two ribbons are 27 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) 27 cm (b) 3 cm (c) 108 cm (d) 9 cm
11. 11.Two bells ring every 12 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 84 min (b) 252 min (c) 3 min (d) 33 min
12. 12.Two ribbons are 44 cm and 77 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) 11 cm (c) 44 cm (d) 33 cm
13. 13.Two bells ring every 18 minutes and every 24 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 42 min (b) 72 min (c) 432 min (d) 6 min
14. 14.Two ribbons are 28 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) 1 cm (d) 7 cm
15. 15.Two ribbons are 18 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) 54 cm (b) 9 cm (c) 3 cm (d) 18 cm
16. 16.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
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) 90 (b) 540 (c) 180 (d) 48
18. 18.Two bells ring every 12 minutes and every 28 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 40 min (b) 84 min (c) 4 min (d) 336 min
19. 19.Two bells ring every 15 minutes and every 20 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 60 min (b) 300 min (c) 5 min (d) 35 min
20. 20.A teacher has 16 pencils and 36 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 20 (b) 2 (c) 4 (d) 16
21. 21.Two ribbons are 30 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) 180 cm (b) 6 cm (c) 30 cm (d) 3 cm
22. 22.A teacher has 33 pencils and 88 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 33 (b) 55 (c) 1 (d) 11
23. 23.Two ribbons are 21 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) 35 cm (b) 7 cm (c) 1 cm (d) 21 cm
24. 24.A teacher has 45 pencils and 63 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 9 (c) 45 (d) 18
25. 25.What is the smallest number of sweets that can be shared equally among 9 children or among 15 children, with none left over? (a) 24 (b) 90 (c) 45 (d) 135
26. 26.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) 27 (c) 9 (d) 3
27. 27.A teacher has 24 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) 3 (c) 30 (d) 24
28. 28.Two ribbons are 36 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) 12 cm (b) 60 cm (c) 36 cm (d) 6 cm
29. 29.Two ribbons are 6 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) 21 cm (b) 1 cm (c) 3 cm (d) 6 cm
30. 30.What is the smallest number of sweets that can be shared equally among 18 children or among 42 children, with none left over? (a) 126 (b) 60 (c) 252 (d) 756
31. 31.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) 96 min (b) 24 min (c) 20 min (d) 4 min
32. 32.A teacher has 48 pencils and 60 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) 48 (d) 240
33. 33.Two ribbons are 8 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) 20 cm (b) 4 cm (c) 2 cm (d) 8 cm
34. 34.What is the smallest number of sweets that can be shared equally among 6 children or among 15 children, with none left over? (a) 60 (b) 30 (c) 21 (d) 90
35. 35.What is the smallest number of sweets that can be shared equally among 12 children or among 14 children, with none left over? (a) 26 (b) 85 (c) 168 (d) 84
36. 36.Two bells ring every 8 minutes and every 10 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 80 min (b) 2 min (c) 18 min (d) 40 min
37. 37.What is the smallest number of sweets that can be shared equally among 12 children or among 16 children, with none left over? (a) 28 (b) 96 (c) 48 (d) 192
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) 50 min (b) 5 min (c) 105 min (d) 525 min
39. 39.What is the smallest number of sweets that can be shared equally among 10 children or among 12 children, with none left over? (a) 22 (b) 120 (c) 60 (d) 61
40. 40.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) 12 cm (b) 2 cm (c) 4 cm (d) 16 cm

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