HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 393 · 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 10 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 2 min (b) 70 min (c) 24 min (d) 140 min
2. 2.Two ribbons are 25 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) 5 cm (b) 25 cm (c) 1 cm (d) 150 cm
3. 3.A teacher has 72 pencils and 81 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 72 (b) 648 (c) 9 (d) 3
4. 4.A teacher has 12 pencils and 18 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) 36 (d) 6
5. 5.A teacher has 44 pencils and 55 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 220 (b) 44 (c) 11 (d) 1
6. 6.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) 756 min (c) 126 min (d) 60 min
7. 7.A teacher has 25 pencils and 30 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 25 (b) 5 (c) 150 (d) 1
8. 8.Two ribbons are 20 cm and 45 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) 1 cm (c) 25 cm (d) 5 cm
9. 9.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) 6 min (b) 72 min (c) 432 min (d) 42 min
10. 10.Two ribbons are 60 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) 6 cm (b) 24 cm (c) 12 cm (d) 60 cm
11. 11.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) 10 min (c) 12 min (d) 2 min
12. 12.Two ribbons are 56 cm and 63 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 504 cm (b) 56 cm (c) 1 cm (d) 7 cm
13. 13.What is the smallest number of sweets that can be shared equally among 10 children or among 15 children, with none left over? (a) 30 (b) 150 (c) 25 (d) 60
14. 14.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) 14 cm (b) 1 cm (c) 7 cm (d) 42 cm
15. 15.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) 1 cm (b) 21 cm (c) 7 cm (d) 84 cm
16. 16.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) 216 min (c) 30 min (d) 6 min
17. 17.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
18. 18.Two ribbons are 25 cm and 40 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) 25 cm (d) 1 cm
19. 19.What is the smallest number of sweets that can be shared equally among 12 children or among 18 children, with none left over? (a) 30 (b) 72 (c) 216 (d) 36
20. 20.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) 42 min (b) 3 min (c) 126 min (d) 27 min
21. 21.Two ribbons are 15 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) 6 cm (b) 3 cm (c) 15 cm (d) 1 cm
22. 22.A teacher has 28 pencils and 63 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 28 (b) 7 (c) 1 (d) 35
23. 23.Two ribbons are 25 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) 25 cm (b) 5 cm (c) 10 cm (d) 1 cm
24. 24.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) 2 (b) 4 (c) 16 (d) 20
25. 25.What is the smallest number of sweets that can be shared equally among 4 children or among 6 children, with none left over? (a) 12 (b) 24 (c) 10 (d) 13
26. 26.What is the smallest number of sweets that can be shared equally among 9 children or among 15 children, with none left over? (a) 90 (b) 135 (c) 24 (d) 45
27. 27.What is the smallest number of sweets that can be shared equally among 10 children or among 12 children, with none left over? (a) 61 (b) 22 (c) 120 (d) 60
28. 28.Two bells ring every 10 minutes and every 35 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 45 min (b) 70 min (c) 350 min (d) 5 min
29. 29.Two bells ring every 8 minutes and every 28 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 36 min (b) 4 min (c) 56 min (d) 224 min
30. 30.What is the smallest number of sweets that can be shared equally among 8 children or among 10 children, with none left over? (a) 18 (b) 80 (c) 40 (d) 41
31. 31.What is the smallest number of sweets that can be shared equally among 8 children or among 12 children, with none left over? (a) 48 (b) 96 (c) 20 (d) 24
32. 32.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) 3 cm (c) 6 cm (d) 30 cm
33. 33.Two bells ring every 12 minutes and every 20 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 240 min (b) 4 min (c) 60 min (d) 32 min
34. 34.Two ribbons are 55 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) 55 cm (c) 11 cm (d) 22 cm
35. 35.Two ribbons are 15 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) 1 cm (b) 15 cm (c) 3 cm (d) 9 cm
36. 36.What is the smallest number of sweets that can be shared equally among 20 children or among 28 children, with none left over? (a) 280 (b) 560 (c) 48 (d) 140
37. 37.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
38. 38.A teacher has 25 pencils and 40 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 25 (b) 1 (c) 15 (d) 5
39. 39.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) 40 min (b) 14 min (c) 2 min (d) 20 min
40. 40.What is the smallest number of sweets that can be shared equally among 10 children or among 35 children, with none left over? (a) 350 (b) 70 (c) 45 (d) 140

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