HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 227 · 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 6 cm and 14 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) 1 cm (c) 6 cm (d) 2 cm
2. 2.A teacher has 6 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) 15 (c) 3 (d) 6
3. 3.What is the smallest number of sweets that can be shared equally among 18 children or among 30 children, with none left over? (a) 540 (b) 48 (c) 180 (d) 90
4. 4.A teacher has 30 pencils and 40 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 5 (b) 10 (c) 120 (d) 30
5. 5.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) 54 cm (b) 378 cm (c) 3 cm (d) 9 cm
6. 6.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) 14 (b) 1 (c) 7 (d) 49
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) 14 min (b) 24 min (c) 2 min (d) 48 min
8. 8.Two ribbons are 10 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) 1 cm (b) 2 cm (c) 8 cm (d) 10 cm
9. 9.What is the smallest number of sweets that can be shared equally among 4 children or among 6 children, with none left over? (a) 10 (b) 13 (c) 12 (d) 24
10. 10.What is the smallest number of sweets that can be shared equally among 12 children or among 14 children, with none left over? (a) 26 (b) 85 (c) 168 (d) 84
11. 11.A teacher has 25 pencils and 40 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 15 (b) 25 (c) 5 (d) 1
12. 12.A teacher has 18 pencils and 27 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 18 (b) 9 (c) 3 (d) 54
13. 13.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) 50 min (b) 5 min (c) 105 min (d) 525 min
14. 14.What is the smallest number of sweets that can be shared equally among 6 children or among 8 children, with none left over? (a) 48 (b) 24 (c) 25 (d) 14
15. 15.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) 33 min (b) 3 min (c) 270 min (d) 90 min
16. 16.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) 42 (c) 126 (d) 27
17. 17.A teacher has 9 pencils and 15 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) 6 (d) 3
18. 18.Two ribbons are 33 cm and 77 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 44 cm (b) 11 cm (c) 1 cm (d) 33 cm
19. 19.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) 42 min (b) 360 min (c) 60 min (d) 6 min
20. 20.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) 120 (d) 60
21. 21.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) 560 cm (b) 70 cm (c) 10 cm (d) 5 cm
22. 22.Two ribbons are 30 cm and 50 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) 20 cm (c) 5 cm (d) 10 cm
23. 23.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) 12 cm (b) 20 cm (c) 2 cm (d) 4 cm
24. 24.What is the smallest number of sweets that can be shared equally among 20 children or among 35 children, with none left over? (a) 140 (b) 55 (c) 280 (d) 700
25. 25.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) 54 min (c) 6 min (d) 84 min
26. 26.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) 192 min (c) 48 min (d) 28 min
27. 27.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) 540 min (b) 48 min (c) 90 min (d) 6 min
28. 28.Two ribbons are 24 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) 72 cm (b) 6 cm (c) 12 cm (d) 24 cm
29. 29.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) 2 min (c) 60 min (d) 30 min
30. 30.Two ribbons are 16 cm and 40 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) 4 cm (c) 24 cm (d) 16 cm
31. 31.Two bells ring every 16 minutes and every 28 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 448 min (b) 44 min (c) 112 min (d) 4 min
32. 32.What is the smallest number of sweets that can be shared equally among 8 children or among 20 children, with none left over? (a) 28 (b) 40 (c) 160 (d) 80
33. 33.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) 60 (c) 31 (d) 30
34. 34.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) 15 min (b) 54 min (c) 3 min (d) 18 min
35. 35.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) 6 min (b) 36 min (c) 216 min (d) 30 min
36. 36.Two ribbons are 8 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) 4 cm (d) 20 cm
37. 37.Two ribbons are 30 cm and 40 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) 120 cm (c) 10 cm (d) 5 cm
38. 38.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) 30 (d) 90
39. 39.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) 126 min (b) 3 min (c) 27 min (d) 42 min
40. 40.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) 50 min (b) 35 min (c) 250 min (d) 5 min

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