HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 46 · 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 15 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 36 min (b) 315 min (c) 105 min (d) 3 min
2. 2.A teacher has 10 pencils and 15 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) 1 (d) 10
3. 3.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) 2 min (c) 42 min (d) 84 min
4. 4.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) 240 (d) 720
5. 5.A teacher has 44 pencils and 77 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 44 (b) 11 (c) 33 (d) 1
6. 6.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) 24 (c) 20 (d) 96
7. 7.Two bells ring every 6 minutes and every 15 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 30 min (b) 90 min (c) 21 min (d) 3 min
8. 8.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) 720 min (c) 6 min (d) 54 min
9. 9.Two bells ring every 6 minutes and every 9 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 3 min (b) 18 min (c) 54 min (d) 15 min
10. 10.Two ribbons are 10 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) 10 cm (b) 25 cm (c) 1 cm (d) 5 cm
11. 11.Two bells ring every 4 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 18 min (b) 2 min (c) 56 min (d) 28 min
12. 12.A teacher has 84 pencils and 96 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) 672 (d) 84
13. 13.Two bells ring every 12 minutes and every 16 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 192 min (b) 28 min (c) 48 min (d) 4 min
14. 14.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) 6 (b) 3 (c) 48 (d) 432
15. 15.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) 216 min (b) 30 min (c) 6 min (d) 36 min
16. 16.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) 2 min (b) 84 min (c) 26 min (d) 168 min
17. 17.Two ribbons are 72 cm and 81 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 648 cm (b) 72 cm (c) 9 cm (d) 3 cm
18. 18.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) 60 min (b) 126 min (c) 756 min (d) 6 min
19. 19.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) 448 (c) 44 (d) 112
20. 20.What is the smallest number of sweets that can be shared equally among 8 children or among 20 children, with none left over? (a) 28 (b) 160 (c) 80 (d) 40
21. 21.A teacher has 18 pencils and 42 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) 24 (d) 18
22. 22.Two ribbons are 30 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) 5 cm (b) 20 cm (c) 30 cm (d) 10 cm
23. 23.Two ribbons are 12 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) 1 cm (b) 3 cm (c) 12 cm (d) 60 cm
24. 24.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) 360 min (b) 6 min (c) 42 min (d) 60 min
25. 25.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) 4 cm (c) 16 cm (d) 2 cm
26. 26.A teacher has 32 pencils and 36 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 288 (b) 32 (c) 4 (d) 2
27. 27.What is the smallest number of sweets that can be shared equally among 10 children or among 25 children, with none left over? (a) 250 (b) 100 (c) 35 (d) 50
28. 28.Two bells ring every 15 minutes and every 18 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 33 min (b) 90 min (c) 270 min (d) 3 min
29. 29.A teacher has 36 pencils and 60 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 24 (b) 36 (c) 6 (d) 12
30. 30.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) 63 min (b) 30 min (c) 3 min (d) 189 min
31. 31.A teacher has 49 pencils and 56 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 7 (c) 392 (d) 49
32. 32.A teacher has 15 pencils and 21 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 15 (b) 6 (c) 1 (d) 3
33. 33.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) 5 (b) 25 (c) 15 (d) 1
34. 34.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) 448 min (b) 4 min (c) 44 min (d) 112 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) 14 cm (c) 1 cm (d) 2 cm
36. 36.What is the smallest number of sweets that can be shared equally among 4 children or among 6 children, with none left over? (a) 10 (b) 24 (c) 12 (d) 13
37. 37.Two ribbons are 72 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) 72 cm (b) 6 cm (c) 504 cm (d) 12 cm
38. 38.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) 56 min (b) 4 min (c) 224 min (d) 36 min
39. 39.A teacher has 15 pencils and 24 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 15 (b) 1 (c) 9 (d) 3
40. 40.What is the smallest number of sweets that can be shared equally among 10 children or among 14 children, with none left over? (a) 71 (b) 70 (c) 140 (d) 24

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