HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 983 · 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 20 minutes and every 24 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 480 min (b) 4 min (c) 44 min (d) 120 min
2. 2.Two bells ring every 15 minutes and every 20 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 300 min (b) 5 min (c) 60 min (d) 35 min
3. 3.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) 14 min (b) 24 min (c) 48 min (d) 2 min
4. 4.Two ribbons are 10 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) 10 cm (b) 5 cm (c) 1 cm (d) 35 cm
5. 5.Two ribbons are 12 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) 20 cm (c) 12 cm (d) 4 cm
6. 6.What is the smallest number of sweets that can be shared equally among 9 children or among 12 children, with none left over? (a) 72 (b) 21 (c) 36 (d) 108
7. 7.Two ribbons are 60 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) 60 cm (b) 36 cm (c) 12 cm (d) 6 cm
8. 8.Two ribbons are 9 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) 9 cm (d) 6 cm
9. 9.Two ribbons are 20 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) 60 cm (c) 20 cm (d) 10 cm
10. 10.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) 4 min (b) 224 min (c) 56 min (d) 36 min
11. 11.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) 2 min (b) 18 min (c) 80 min (d) 40 min
12. 12.A teacher has 56 pencils and 63 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 56 (b) 504 (c) 7 (d) 1
13. 13.What is the smallest number of sweets that can be shared equally among 10 children or among 12 children, with none left over? (a) 120 (b) 61 (c) 60 (d) 22
14. 14.What is the smallest number of sweets that can be shared equally among 15 children or among 18 children, with none left over? (a) 33 (b) 180 (c) 270 (d) 90
15. 15.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) 140 min (c) 24 min (d) 70 min
16. 16.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) 6 min (b) 540 min (c) 48 min (d) 90 min
17. 17.What is the smallest number of sweets that can be shared equally among 6 children or among 15 children, with none left over? (a) 21 (b) 60 (c) 90 (d) 30
18. 18.A teacher has 16 pencils and 28 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 2 (b) 12 (c) 4 (d) 16
19. 19.A teacher has 22 pencils and 55 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 33 (b) 11 (c) 22 (d) 1
20. 20.Two ribbons are 33 cm and 55 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 22 cm (b) 33 cm (c) 11 cm (d) 1 cm
21. 21.A teacher has 20 pencils and 32 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 4 (b) 12 (c) 20 (d) 2
22. 22.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) 2 min (b) 14 min (c) 40 min (d) 20 min
23. 23.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) 60 cm (b) 6 cm (c) 360 cm (d) 12 cm
24. 24.A teacher has 15 pencils and 25 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 10 (b) 5 (c) 15 (d) 1
25. 25.A teacher has 10 pencils and 25 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 15 (b) 5 (c) 1 (d) 10
26. 26.What is the smallest number of sweets that can be shared equally among 6 children or among 9 children, with none left over? (a) 54 (b) 15 (c) 18 (d) 36
27. 27.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) 150 (d) 75
28. 28.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) 84 cm (b) 7 cm (c) 21 cm (d) 1 cm
29. 29.Two ribbons are 15 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) 20 cm (b) 5 cm (c) 1 cm (d) 15 cm
30. 30.Two bells ring every 20 minutes and every 35 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 700 min (b) 5 min (c) 55 min (d) 140 min
31. 31.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) 2 (b) 6 (c) 1 (d) 24
32. 32.A teacher has 14 pencils and 63 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 49 (c) 7 (d) 14
33. 33.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) 504 min (b) 6 min (c) 54 min (d) 84 min
34. 34.A teacher has 12 pencils and 14 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) 84 (d) 2
35. 35.What is the smallest number of sweets that can be shared equally among 18 children or among 42 children, with none left over? (a) 756 (b) 252 (c) 60 (d) 126
36. 36.A teacher has 60 pencils and 72 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 60 (c) 12 (d) 360
37. 37.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) 12 cm (d) 20 cm
38. 38.What is the smallest number of sweets that can be shared equally among 6 children or among 10 children, with none left over? (a) 16 (b) 31 (c) 30 (d) 60
39. 39.Two ribbons are 21 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) 6 cm (b) 21 cm (c) 1 cm (d) 3 cm
40. 40.Two ribbons are 16 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) 56 cm (b) 16 cm (c) 8 cm (d) 4 cm

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