HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 464 · 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 44 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) 1 cm (b) 220 cm (c) 11 cm (d) 44 cm
2. 2.A teacher has 8 pencils and 18 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 2 (b) 10 (c) 1 (d) 8
3. 3.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) 500 min (b) 100 min (c) 45 min (d) 5 min
4. 4.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) 30 min (b) 2 min (c) 16 min (d) 60 min
5. 5.A teacher has 40 pencils and 45 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 360 (b) 40 (c) 5 (d) 1
6. 6.What is the smallest number of sweets that can be shared equally among 6 children or among 21 children, with none left over? (a) 27 (b) 42 (c) 126 (d) 84
7. 7.Two ribbons are 45 cm and 81 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 45 cm (b) 36 cm (c) 3 cm (d) 9 cm
8. 8.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) 2 cm (c) 1 cm (d) 6 cm
9. 9.What is the smallest number of sweets that can be shared equally among 8 children or among 12 children, with none left over? (a) 20 (b) 96 (c) 24 (d) 48
10. 10.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) 60 (c) 126 (d) 252
11. 11.A teacher has 32 pencils and 40 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 160 (b) 4 (c) 8 (d) 32
12. 12.What is the smallest number of sweets that can be shared equally among 10 children or among 14 children, with none left over? (a) 70 (b) 71 (c) 140 (d) 24
13. 13.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) 1 (b) 5 (c) 10 (d) 25
14. 14.What is the smallest number of sweets that can be shared equally among 8 children or among 14 children, with none left over? (a) 57 (b) 56 (c) 22 (d) 112
15. 15.Two bells ring every 4 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 18 min (b) 56 min (c) 2 min (d) 28 min
16. 16.Two bells ring every 10 minutes and every 12 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 120 min (b) 22 min (c) 2 min (d) 60 min
17. 17.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) 108 (c) 21 (d) 36
18. 18.What is the smallest number of sweets that can be shared equally among 4 children or among 6 children, with none left over? (a) 12 (b) 10 (c) 13 (d) 24
19. 19.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) 7 cm (b) 56 cm (c) 1 cm (d) 504 cm
20. 20.What is the smallest number of sweets that can be shared equally among 12 children or among 14 children, with none left over? (a) 85 (b) 168 (c) 84 (d) 26
21. 21.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) 8 cm (c) 48 cm (d) 4 cm
22. 22.A teacher has 50 pencils and 80 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) 30 (d) 50
23. 23.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) 32 min (b) 60 min (c) 240 min (d) 4 min
24. 24.A teacher has 6 pencils and 10 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) 4 (d) 1
25. 25.Two ribbons are 6 cm and 8 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 24 cm (b) 1 cm (c) 6 cm (d) 2 cm
26. 26.A teacher has 20 pencils and 24 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 120 (b) 4 (c) 2 (d) 20
27. 27.A teacher has 35 pencils and 56 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 35 (b) 21 (c) 7 (d) 1
28. 28.What is the smallest number of sweets that can be shared equally among 12 children or among 20 children, with none left over? (a) 240 (b) 32 (c) 120 (d) 60
29. 29.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) 150 min (b) 5 min (c) 30 min (d) 25 min
30. 30.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) 3 (b) 9 (c) 63 (d) 504
31. 31.What is the smallest number of sweets that can be shared equally among 6 children or among 14 children, with none left over? (a) 43 (b) 20 (c) 84 (d) 42
32. 32.Two bells ring every 4 minutes and every 6 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 12 min (b) 24 min (c) 2 min (d) 10 min
33. 33.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) 120 cm (b) 30 cm (c) 5 cm (d) 10 cm
34. 34.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) 3 cm (b) 21 cm (c) 6 cm (d) 1 cm
35. 35.Two bells ring every 12 minutes and every 28 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 84 min (b) 4 min (c) 336 min (d) 40 min
36. 36.Two ribbons are 45 cm and 54 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 45 cm (b) 3 cm (c) 9 cm (d) 270 cm
37. 37.Two ribbons are 28 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) 35 cm (b) 7 cm (c) 1 cm (d) 28 cm
38. 38.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) 36 min (b) 6 min (c) 30 min (d) 216 min
39. 39.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) 12 (c) 60 (d) 360
40. 40.A teacher has 14 pencils and 16 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 112 (b) 2 (c) 1 (d) 14

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