HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 384 · 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 8 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 22 min (b) 112 min (c) 2 min (d) 56 min
2. 2.What is the smallest number of sweets that can be shared equally among 18 children or among 30 children, with none left over? (a) 540 (b) 90 (c) 180 (d) 48
3. 3.Two ribbons are 24 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) 168 cm (b) 24 cm (c) 4 cm (d) 2 cm
4. 4.A teacher has 6 pencils and 16 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 2 (b) 6 (c) 10 (d) 1
5. 5.A teacher has 18 pencils and 48 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 18 (b) 6 (c) 3 (d) 30
6. 6.Two ribbons are 8 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) 12 cm (b) 8 cm (c) 4 cm (d) 2 cm
7. 7.Two bells ring every 16 minutes and every 20 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 320 min (b) 4 min (c) 36 min (d) 80 min
8. 8.What is the smallest number of sweets that can be shared equally among 16 children or among 28 children, with none left over? (a) 112 (b) 44 (c) 448 (d) 224
9. 9.Two bells ring every 18 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 378 min (b) 3 min (c) 39 min (d) 126 min
10. 10.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) 54 min (b) 6 min (c) 120 min (d) 720 min
11. 11.A teacher has 55 pencils and 66 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 11 (b) 1 (c) 55 (d) 330
12. 12.Two ribbons are 16 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) 8 cm (b) 48 cm (c) 16 cm (d) 4 cm
13. 13.Two ribbons are 42 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) 42 cm (b) 294 cm (c) 1 cm (d) 7 cm
14. 14.Two ribbons are 60 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) 6 cm (b) 12 cm (c) 360 cm (d) 60 cm
15. 15.Two ribbons are 16 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) 16 cm (c) 2 cm (d) 4 cm
16. 16.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) 6 min (c) 126 min (d) 756 min
17. 17.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) 3 min (b) 42 min (c) 27 min (d) 126 min
18. 18.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) 135 min (b) 45 min (c) 24 min (d) 3 min
19. 19.Two ribbons are 44 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) 44 cm (b) 11 cm (c) 1 cm (d) 55 cm
20. 20.What is the smallest number of sweets that can be shared equally among 15 children or among 25 children, with none left over? (a) 75 (b) 375 (c) 150 (d) 40
21. 21.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) 56 min (c) 224 min (d) 4 min
22. 22.A teacher has 35 pencils and 42 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 35 (c) 210 (d) 7
23. 23.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) 1 cm (b) 3 cm (c) 15 cm (d) 9 cm
24. 24.What is the smallest number of sweets that can be shared equally among 24 children or among 30 children, with none left over? (a) 240 (b) 54 (c) 720 (d) 120
25. 25.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) 8 (b) 28 (c) 4 (d) 2
26. 26.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) 2 min (b) 60 min (c) 30 min (d) 16 min
27. 27.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) 22 (b) 1 (c) 11 (d) 77
28. 28.Two bells ring every 15 minutes and every 25 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 40 min (b) 375 min (c) 75 min (d) 5 min
29. 29.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) 432 (b) 3 (c) 48 (d) 6
30. 30.What is the smallest number of sweets that can be shared equally among 6 children or among 10 children, with none left over? (a) 60 (b) 31 (c) 30 (d) 16
31. 31.A teacher has 27 pencils and 36 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 9 (b) 3 (c) 27 (d) 108
32. 32.What is the smallest number of sweets that can be shared equally among 15 children or among 35 children, with none left over? (a) 105 (b) 50 (c) 210 (d) 525
33. 33.A teacher has 10 pencils and 14 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 4 (b) 2 (c) 1 (d) 10
34. 34.Two ribbons are 18 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) 18 cm (b) 3 cm (c) 72 cm (d) 6 cm
35. 35.A teacher has 6 pencils and 9 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 18 (b) 3 (c) 1 (d) 6
36. 36.What is the smallest number of sweets that can be shared equally among 8 children or among 28 children, with none left over? (a) 56 (b) 112 (c) 36 (d) 224
37. 37.A teacher has 4 pencils and 10 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 1 (c) 4 (d) 2
38. 38.What is the smallest number of sweets that can be shared equally among 12 children or among 30 children, with none left over? (a) 360 (b) 120 (c) 42 (d) 60
39. 39.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) 6 (b) 48 (c) 12 (d) 240
40. 40.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) 105 min (b) 36 min (c) 3 min (d) 315 min

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