HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 299 · 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 ribbons are 8 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) 28 cm (b) 2 cm (c) 8 cm (d) 4 cm
2. 2.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) 6 (b) 12 (c) 24 (d) 36
3. 3.A teacher has 30 pencils and 80 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 30 (b) 5 (c) 10 (d) 50
4. 4.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) 392 (b) 1 (c) 7 (d) 49
5. 5.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) 30 min (b) 63 min (c) 3 min (d) 189 min
6. 6.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) 3 min (b) 36 min (c) 315 min (d) 105 min
7. 7.Two ribbons are 12 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) 6 cm (b) 12 cm (c) 36 cm (d) 3 cm
8. 8.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) 5 min (b) 30 min (c) 25 min (d) 150 min
9. 9.Two bells ring every 10 minutes and every 25 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 5 min (b) 250 min (c) 35 min (d) 50 min
10. 10.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) 6 min (c) 432 min (d) 72 min
11. 11.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) 4 min (b) 28 min (c) 192 min (d) 48 min
12. 12.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
13. 13.What is the smallest number of sweets that can be shared equally among 10 children or among 14 children, with none left over? (a) 140 (b) 70 (c) 24 (d) 71
14. 14.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) 30 min (c) 2 min (d) 60 min
15. 15.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) 3 min (d) 21 min
16. 16.A teacher has 40 pencils and 64 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 4 (b) 40 (c) 8 (d) 24
17. 17.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) 18 min (b) 3 min (c) 15 min (d) 54 min
18. 18.Two bells ring every 12 minutes and every 42 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 54 min (b) 6 min (c) 504 min (d) 84 min
19. 19.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) 648 (b) 3 (c) 9 (d) 72
20. 20.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) 350 min (b) 45 min (c) 70 min (d) 5 min
21. 21.Two ribbons are 20 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) 120 cm (b) 2 cm (c) 20 cm (d) 4 cm
22. 22.A teacher has 22 pencils and 33 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 66 (c) 11 (d) 22
23. 23.Two ribbons are 20 cm and 32 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 2 cm (b) 4 cm (c) 20 cm (d) 12 cm
24. 24.Two ribbons are 16 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) 2 cm (b) 20 cm (c) 16 cm (d) 4 cm
25. 25.Two bells ring every 18 minutes and every 30 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 90 min (b) 540 min (c) 6 min (d) 48 min
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) 4 (b) 288 (c) 2 (d) 32
27. 27.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) 3 min (b) 24 min (c) 135 min (d) 45 min
28. 28.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) 216 cm (b) 1 cm (c) 3 cm (d) 24 cm
29. 29.Two ribbons are 20 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) 20 cm (b) 5 cm (c) 1 cm (d) 100 cm
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) 41 (d) 40
31. 31.What is the smallest number of sweets that can be shared equally among 4 children or among 6 children, with none left over? (a) 13 (b) 12 (c) 10 (d) 24
32. 32.A teacher has 24 pencils and 30 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 24 (b) 6 (c) 120 (d) 3
33. 33.Two ribbons are 45 cm and 54 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 270 cm (b) 9 cm (c) 3 cm (d) 45 cm
34. 34.What is the smallest number of sweets that can be shared equally among 15 children or among 25 children, with none left over? (a) 40 (b) 150 (c) 375 (d) 75
35. 35.What is the smallest number of sweets that can be shared equally among 9 children or among 21 children, with none left over? (a) 126 (b) 189 (c) 30 (d) 63
36. 36.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) 105 (c) 315 (d) 210
37. 37.A teacher has 30 pencils and 70 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 30 (b) 5 (c) 40 (d) 10
38. 38.A teacher has 70 pencils and 90 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 20 (b) 5 (c) 10 (d) 70
39. 39.What is the smallest number of sweets that can be shared equally among 6 children or among 14 children, with none left over? (a) 84 (b) 43 (c) 20 (d) 42
40. 40.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) 168 min (b) 26 min (c) 84 min (d) 2 min

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