HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 927 · 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 8 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) 8 cm (b) 28 cm (c) 2 cm (d) 4 cm
2. 2.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) 40 (c) 24 (d) 8
3. 3.A teacher has 48 pencils and 84 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 12 (b) 36 (c) 6 (d) 48
4. 4.What is the smallest number of sweets that can be shared equally among 10 children or among 12 children, with none left over? (a) 22 (b) 60 (c) 120 (d) 61
5. 5.A teacher has 10 pencils and 35 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 25 (b) 10 (c) 5 (d) 1
6. 6.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) 16 (d) 4
7. 7.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) 30 min (b) 150 min (c) 5 min (d) 25 min
8. 8.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) 1 cm (c) 14 cm (d) 7 cm
9. 9.Two bells ring every 6 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 2 min (b) 20 min (c) 42 min (d) 84 min
10. 10.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
11. 11.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) 6 min (c) 36 min (d) 30 min
12. 12.Two ribbons are 49 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) 1 cm (b) 7 cm (c) 14 cm (d) 49 cm
13. 13.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
14. 14.What is the smallest number of sweets that can be shared equally among 10 children or among 15 children, with none left over? (a) 60 (b) 150 (c) 30 (d) 25
15. 15.What is the smallest number of sweets that can be shared equally among 4 children or among 10 children, with none left over? (a) 20 (b) 14 (c) 21 (d) 40
16. 16.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) 60 min (c) 30 min (d) 2 min
17. 17.A teacher has 63 pencils and 72 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 63 (b) 3 (c) 504 (d) 9
18. 18.Two ribbons are 36 cm and 84 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) 12 cm (d) 48 cm
19. 19.Two bells ring every 20 minutes and every 28 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 140 min (b) 4 min (c) 48 min (d) 560 min
20. 20.What is the smallest number of sweets that can be shared equally among 8 children or among 12 children, with none left over? (a) 96 (b) 20 (c) 48 (d) 24
21. 21.A teacher has 14 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) 4 (c) 14 (d) 2
22. 22.A teacher has 35 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
23. 23.What is the smallest number of sweets that can be shared equally among 6 children or among 14 children, with none left over? (a) 42 (b) 43 (c) 20 (d) 84
24. 24.What is the smallest number of sweets that can be shared equally among 9 children or among 15 children, with none left over? (a) 24 (b) 90 (c) 135 (d) 45
25. 25.What is the smallest number of sweets that can be shared equally among 4 children or among 14 children, with none left over? (a) 18 (b) 29 (c) 56 (d) 28
26. 26.Two ribbons are 6 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
27. 27.What is the smallest number of sweets that can be shared equally among 15 children or among 21 children, with none left over? (a) 105 (b) 315 (c) 210 (d) 36
28. 28.A teacher has 63 pencils and 81 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 63 (b) 3 (c) 9 (d) 18
29. 29.Two ribbons are 8 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) 4 cm (b) 24 cm (c) 8 cm (d) 2 cm
30. 30.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) 1 cm (b) 15 cm (c) 5 cm (d) 20 cm
31. 31.Two bells ring every 20 minutes and every 25 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 45 min (b) 100 min (c) 5 min (d) 500 min
32. 32.Two bells ring every 12 minutes and every 20 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 240 min (b) 32 min (c) 60 min (d) 4 min
33. 33.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) 180 (d) 48
34. 34.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) 480 min (c) 44 min (d) 120 min
35. 35.What is the smallest number of sweets that can be shared equally among 9 children or among 21 children, with none left over? (a) 63 (b) 126 (c) 189 (d) 30
36. 36.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) 3 min (b) 270 min (c) 33 min (d) 90 min
37. 37.A teacher has 44 pencils and 99 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 55 (c) 44 (d) 11
38. 38.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) 56 min (b) 4 min (c) 224 min (d) 36 min
39. 39.A teacher has 9 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) 12 (c) 3 (d) 9
40. 40.Two ribbons are 16 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) 16 cm (b) 48 cm (c) 8 cm (d) 4 cm

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