HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 788 · 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.What is the smallest number of sweets that can be shared equally among 18 children or among 21 children, with none left over? (a) 39 (b) 252 (c) 378 (d) 126
2. 2.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) 5 cm (c) 10 cm (d) 1 cm
3. 3.A teacher has 9 pencils and 24 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 1 (c) 15 (d) 9
4. 4.A teacher has 27 pencils and 45 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 27 (b) 9 (c) 18 (d) 3
5. 5.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) 36 cm (b) 6 cm (c) 24 cm (d) 12 cm
6. 6.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) 21 min (c) 36 min (d) 108 min
7. 7.Two ribbons are 24 cm and 42 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) 3 cm (c) 24 cm (d) 6 cm
8. 8.A teacher has 48 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) 48 (c) 432 (d) 6
9. 9.What is the smallest number of sweets that can be shared equally among 8 children or among 12 children, with none left over? (a) 24 (b) 96 (c) 48 (d) 20
10. 10.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) 45 min (c) 135 min (d) 3 min
11. 11.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) 10 cm (b) 50 cm (c) 40 cm (d) 5 cm
12. 12.Two ribbons are 24 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) 12 cm (b) 36 cm (c) 24 cm (d) 6 cm
13. 13.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) 120 (c) 720 (d) 240
14. 14.What is the smallest number of sweets that can be shared equally among 15 children or among 21 children, with none left over? (a) 36 (b) 315 (c) 105 (d) 210
15. 15.Two ribbons are 55 cm and 99 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) 55 cm (d) 44 cm
16. 16.Two ribbons are 6 cm and 15 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) 9 cm (d) 3 cm
17. 17.What is the smallest number of sweets that can be shared equally among 10 children or among 35 children, with none left over? (a) 70 (b) 45 (c) 140 (d) 350
18. 18.A teacher has 36 pencils and 81 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 45 (b) 36 (c) 9 (d) 3
19. 19.What is the smallest number of sweets that can be shared equally among 18 children or among 42 children, with none left over? (a) 60 (b) 252 (c) 126 (d) 756
20. 20.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) 20 min (c) 96 min (d) 4 min
21. 21.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) 25 min (b) 150 min (c) 30 min (d) 5 min
22. 22.Two ribbons are 40 cm and 50 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 40 cm (b) 10 cm (c) 200 cm (d) 5 cm
23. 23.Two ribbons are 18 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) 126 cm (c) 18 cm (d) 3 cm
24. 24.What is the smallest number of sweets that can be shared equally among 12 children or among 15 children, with none left over? (a) 60 (b) 27 (c) 180 (d) 120
25. 25.Two ribbons are 6 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) 6 cm (c) 15 cm (d) 3 cm
26. 26.What is the smallest number of sweets that can be shared equally among 18 children or among 30 children, with none left over? (a) 48 (b) 180 (c) 90 (d) 540
27. 27.What is the smallest number of sweets that can be shared equally among 10 children or among 15 children, with none left over? (a) 60 (b) 150 (c) 30 (d) 25
28. 28.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) 56 min (b) 2 min (c) 112 min (d) 22 min
29. 29.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) 432 (c) 72 (d) 144
30. 30.A teacher has 25 pencils and 45 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 5 (b) 20 (c) 25 (d) 1
31. 31.A teacher has 40 pencils and 70 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) 30 (d) 40
32. 32.Two ribbons are 48 cm and 84 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) 6 cm (c) 36 cm (d) 12 cm
33. 33.Two ribbons are 55 cm and 66 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) 330 cm (c) 55 cm (d) 11 cm
34. 34.Two ribbons are 9 cm and 24 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) 9 cm (d) 3 cm
35. 35.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) 2 min (b) 84 min (c) 20 min (d) 42 min
36. 36.Two ribbons are 36 cm and 42 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) 3 cm (c) 252 cm (d) 6 cm
37. 37.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) 12 (b) 3 (c) 9 (d) 1
38. 38.Two bells ring every 20 minutes and every 35 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 700 min (b) 5 min (c) 55 min (d) 140 min
39. 39.A teacher has 28 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) 28 (d) 8
40. 40.Two ribbons are 21 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) 21 cm (b) 7 cm (c) 84 cm (d) 1 cm

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