HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 76 · 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 12 cm and 16 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) 48 cm (c) 12 cm (d) 4 cm
2. 2.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) 21 min (b) 3 min (c) 90 min (d) 30 min
3. 3.Two ribbons are 40 cm and 90 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 50 cm (b) 10 cm (c) 5 cm (d) 40 cm
4. 4.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) 16 cm (c) 2 cm (d) 4 cm
5. 5.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) 45 min (b) 70 min (c) 5 min (d) 350 min
6. 6.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) 15 min (d) 54 min
7. 7.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) 48 min (c) 14 min (d) 2 min
8. 8.Two bells ring every 25 minutes and every 30 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 5 min (b) 55 min (c) 750 min (d) 150 min
9. 9.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) 35 cm (b) 10 cm (c) 1 cm (d) 5 cm
10. 10.A teacher has 30 pencils and 35 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) 210 (d) 1
11. 11.Two ribbons are 18 cm and 21 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 126 cm (b) 1 cm (c) 18 cm (d) 3 cm
12. 12.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) 60 min (d) 42 min
13. 13.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
14. 14.A teacher has 12 pencils and 18 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 36 (b) 6 (c) 3 (d) 12
15. 15.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) 15 cm (b) 1 cm (c) 9 cm (d) 3 cm
16. 16.Two ribbons are 21 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) 7 cm (b) 1 cm (c) 21 cm (d) 14 cm
17. 17.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) 42 (c) 60 (d) 120
18. 18.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) 25 min (c) 30 min (d) 150 min
19. 19.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) 126 min (c) 756 min (d) 60 min
20. 20.What is the smallest number of sweets that can be shared equally among 4 children or among 6 children, with none left over? (a) 24 (b) 12 (c) 13 (d) 10
21. 21.Two ribbons are 12 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) 1 cm (b) 3 cm (c) 12 cm (d) 15 cm
22. 22.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) 5 min (b) 140 min (c) 700 min (d) 55 min
23. 23.What is the smallest number of sweets that can be shared equally among 20 children or among 24 children, with none left over? (a) 120 (b) 44 (c) 480 (d) 240
24. 24.Two ribbons are 32 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) 40 cm (b) 4 cm (c) 8 cm (d) 32 cm
25. 25.Two ribbons are 84 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) 12 cm (b) 84 cm (c) 672 cm (d) 6 cm
26. 26.A teacher has 27 pencils and 72 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) 27 (d) 45
27. 27.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) 12 cm (c) 6 cm (d) 36 cm
28. 28.What is the smallest number of sweets that can be shared equally among 12 children or among 21 children, with none left over? (a) 168 (b) 33 (c) 84 (d) 252
29. 29.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) 15 (d) 18
30. 30.Two ribbons are 54 cm and 63 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) 3 cm (c) 54 cm (d) 378 cm
31. 31.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) 3 cm (c) 18 cm (d) 54 cm
32. 32.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) 10 cm (c) 60 cm (d) 20 cm
33. 33.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) 80 min (c) 18 min (d) 40 min
34. 34.Two bells ring every 12 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 33 min (b) 84 min (c) 252 min (d) 3 min
35. 35.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) 1 (b) 3 (c) 36 (d) 9
36. 36.What is the smallest number of sweets that can be shared equally among 10 children or among 12 children, with none left over? (a) 61 (b) 120 (c) 22 (d) 60
37. 37.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) 56 min (b) 22 min (c) 112 min (d) 2 min
38. 38.Two ribbons are 70 cm and 80 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) 560 cm (c) 70 cm (d) 10 cm
39. 39.What is the smallest number of sweets that can be shared equally among 15 children or among 25 children, with none left over? (a) 150 (b) 40 (c) 75 (d) 375
40. 40.What is the smallest number of sweets that can be shared equally among 6 children or among 10 children, with none left over? (a) 30 (b) 16 (c) 31 (d) 60

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