HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 507 · 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 12 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 3 min (b) 252 min (c) 33 min (d) 84 min
2. 2.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) 18 cm (c) 3 cm (d) 1 cm
3. 3.A teacher has 15 pencils and 21 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) 6 (d) 15
4. 4.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) 8 (c) 24 (d) 40
5. 5.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) 2 min (d) 84 min
6. 6.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) 350 min (d) 5 min
7. 7.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) 1 cm (c) 9 cm (d) 36 cm
8. 8.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) 36 min (b) 80 min (c) 4 min (d) 320 min
9. 9.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) 375 min (b) 5 min (c) 75 min (d) 40 min
10. 10.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) 504 min (c) 84 min (d) 6 min
11. 11.Two ribbons are 80 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) 80 cm (b) 720 cm (c) 10 cm (d) 5 cm
12. 12.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) 11 (b) 22 (c) 77 (d) 1
13. 13.What is the smallest number of sweets that can be shared equally among 20 children or among 35 children, with none left over? (a) 700 (b) 55 (c) 280 (d) 140
14. 14.A teacher has 10 pencils and 45 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) 1 (d) 35
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) 140 min (b) 2 min (c) 24 min (d) 70 min
16. 16.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) 40 min (c) 20 min (d) 14 min
17. 17.A teacher has 15 pencils and 27 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) 3 (d) 15
18. 18.Two ribbons are 22 cm and 33 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) 66 cm (c) 22 cm (d) 11 cm
19. 19.Two ribbons are 50 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) 30 cm (b) 10 cm (c) 5 cm (d) 50 cm
20. 20.A teacher has 12 pencils and 15 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 12 (c) 1 (d) 60
21. 21.A teacher has 12 pencils and 32 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 12 (b) 2 (c) 20 (d) 4
22. 22.A teacher has 4 pencils and 18 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 2 (c) 14 (d) 4
23. 23.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) 27 min (b) 126 min (c) 42 min (d) 3 min
24. 24.Two bells ring every 12 minutes and every 15 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 60 min (b) 3 min (c) 180 min (d) 27 min
25. 25.A teacher has 14 pencils and 21 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 7 (b) 1 (c) 14 (d) 42
26. 26.What is the smallest number of sweets that can be shared equally among 12 children or among 28 children, with none left over? (a) 168 (b) 336 (c) 84 (d) 40
27. 27.What is the smallest number of sweets that can be shared equally among 12 children or among 21 children, with none left over? (a) 33 (b) 252 (c) 168 (d) 84
28. 28.What is the smallest number of sweets that can be shared equally among 4 children or among 10 children, with none left over? (a) 14 (b) 21 (c) 40 (d) 20
29. 29.A teacher has 15 pencils and 18 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 90 (b) 3 (c) 1 (d) 15
30. 30.A teacher has 45 pencils and 54 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) 45 (d) 270
31. 31.Two bells ring every 15 minutes and every 35 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 525 min (b) 105 min (c) 5 min (d) 50 min
32. 32.Two ribbons are 56 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) 56 cm (b) 504 cm (c) 7 cm (d) 1 cm
33. 33.Two ribbons are 14 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) 21 cm (b) 14 cm (c) 7 cm (d) 1 cm
34. 34.A teacher has 16 pencils and 18 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 144 (c) 16 (d) 2
35. 35.What is the smallest number of sweets that can be shared equally among 9 children or among 15 children, with none left over? (a) 90 (b) 45 (c) 135 (d) 24
36. 36.Two ribbons are 40 cm and 48 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 240 cm (b) 40 cm (c) 4 cm (d) 8 cm
37. 37.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) 12 cm (b) 15 cm (c) 3 cm (d) 1 cm
38. 38.What is the smallest number of sweets that can be shared equally among 10 children or among 14 children, with none left over? (a) 71 (b) 140 (c) 70 (d) 24
39. 39.What is the smallest number of sweets that can be shared equally among 8 children or among 20 children, with none left over? (a) 80 (b) 40 (c) 28 (d) 160
40. 40.Two ribbons are 32 cm and 56 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 4 cm (b) 8 cm (c) 24 cm (d) 32 cm

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