HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 56 · 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.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) 672 (b) 84 (c) 6 (d) 12
2. 2.What is the smallest number of sweets that can be shared equally among 15 children or among 25 children, with none left over? (a) 375 (b) 40 (c) 75 (d) 150
3. 3.Two bells ring every 8 minutes and every 10 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 18 min (b) 80 min (c) 40 min (d) 2 min
4. 4.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) 60 min (b) 6 min (c) 42 min (d) 360 min
5. 5.Two ribbons are 20 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) 8 cm (b) 2 cm (c) 20 cm (d) 4 cm
6. 6.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) 30 (b) 10 (c) 5 (d) 40
7. 7.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) 48 min (b) 28 min (c) 192 min (d) 4 min
8. 8.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
9. 9.Two ribbons are 9 cm and 12 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 3 cm (b) 9 cm (c) 1 cm (d) 36 cm
10. 10.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) 36 min (c) 6 min (d) 30 min
11. 11.What is the smallest number of sweets that can be shared equally among 18 children or among 30 children, with none left over? (a) 90 (b) 540 (c) 48 (d) 180
12. 12.A teacher has 15 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) 15 (c) 5 (d) 1
13. 13.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) 96 min (b) 24 min (c) 4 min (d) 20 min
14. 14.What is the smallest number of sweets that can be shared equally among 6 children or among 9 children, with none left over? (a) 36 (b) 54 (c) 18 (d) 15
15. 15.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) 6 min (b) 54 min (c) 504 min (d) 84 min
16. 16.Two ribbons are 4 cm and 6 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) 4 cm (c) 2 cm (d) 12 cm
17. 17.What is the smallest number of sweets that can be shared equally among 9 children or among 12 children, with none left over? (a) 21 (b) 108 (c) 72 (d) 36
18. 18.A teacher has 4 pencils and 6 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 12 (b) 1 (c) 2 (d) 4
19. 19.A teacher has 16 pencils and 72 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 4 (b) 56 (c) 8 (d) 16
20. 20.Two bells ring every 6 minutes and every 8 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 24 min (b) 14 min (c) 2 min (d) 48 min
21. 21.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) 26 min (b) 168 min (c) 84 min (d) 2 min
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.A teacher has 45 pencils and 63 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 9 (c) 45 (d) 18
24. 24.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) 20 (b) 25 (c) 5 (d) 1
25. 25.Two bells ring every 10 minutes and every 12 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 2 min (b) 60 min (c) 120 min (d) 22 min
26. 26.Two ribbons are 18 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) 9 cm (b) 54 cm (c) 18 cm (d) 3 cm
27. 27.What is the smallest number of sweets that can be shared equally among 6 children or among 21 children, with none left over? (a) 84 (b) 126 (c) 27 (d) 42
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) 270 min (b) 3 min (c) 33 min (d) 90 min
29. 29.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) 150 min (b) 5 min (c) 25 min (d) 30 min
30. 30.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) 60 min (d) 126 min
31. 31.A teacher has 9 pencils and 12 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 9 (b) 1 (c) 36 (d) 3
32. 32.A teacher has 8 pencils and 28 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 8 (b) 20 (c) 2 (d) 4
33. 33.Two bells ring every 20 minutes and every 24 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 4 min (b) 44 min (c) 480 min (d) 120 min
34. 34.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) 4 min (b) 36 min (c) 320 min (d) 80 min
35. 35.A teacher has 6 pencils and 8 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 6 (c) 24 (d) 2
36. 36.Two ribbons are 63 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) 3 cm (b) 9 cm (c) 63 cm (d) 18 cm
37. 37.Two ribbons are 10 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) 10 cm (b) 1 cm (c) 5 cm (d) 30 cm
38. 38.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) 7 (c) 49 (d) 1
39. 39.Two ribbons are 36 cm and 96 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) 36 cm (c) 60 cm (d) 12 cm
40. 40.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) 2 min (b) 112 min (c) 56 min (d) 22 min

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