HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 824 · 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 32 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) 160 cm (c) 32 cm (d) 4 cm
2. 2.Two ribbons are 36 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) 12 cm (b) 6 cm (c) 144 cm (d) 36 cm
3. 3.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) 1 cm (c) 5 cm (d) 10 cm
4. 4.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) 1 cm (b) 44 cm (c) 11 cm (d) 33 cm
5. 5.What is the smallest number of sweets that can be shared equally among 10 children or among 35 children, with none left over? (a) 45 (b) 140 (c) 350 (d) 70
6. 6.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) 48 (c) 96 (d) 24
7. 7.A teacher has 44 pencils and 55 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 220 (b) 1 (c) 11 (d) 44
8. 8.A teacher has 56 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) 56 (c) 8 (d) 448
9. 9.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) 22 min (b) 2 min (c) 120 min (d) 60 min
10. 10.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) 8 (b) 40 (c) 4 (d) 24
11. 11.Two ribbons are 24 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) 24 cm (b) 4 cm (c) 16 cm (d) 8 cm
12. 12.A teacher has 6 pencils and 15 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 6 (c) 9 (d) 3
13. 13.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) 5 cm (b) 30 cm (c) 10 cm (d) 50 cm
14. 14.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) 126 (c) 84 (d) 42
15. 15.What is the smallest number of sweets that can be shared equally among 15 children or among 20 children, with none left over? (a) 120 (b) 300 (c) 35 (d) 60
16. 16.Two ribbons are 18 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) 18 cm (b) 9 cm (c) 45 cm (d) 3 cm
17. 17.Two ribbons are 30 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) 6 cm (b) 30 cm (c) 180 cm (d) 3 cm
18. 18.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) 8 cm (b) 16 cm (c) 48 cm (d) 4 cm
19. 19.Two bells ring every 9 minutes and every 15 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 135 min (b) 45 min (c) 3 min (d) 24 min
20. 20.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) 60 min (b) 6 min (c) 756 min (d) 126 min
21. 21.A teacher has 32 pencils and 56 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 4 (b) 32 (c) 24 (d) 8
22. 22.What is the smallest number of sweets that can be shared equally among 18 children or among 42 children, with none left over? (a) 60 (b) 756 (c) 252 (d) 126
23. 23.What is the smallest number of sweets that can be shared equally among 12 children or among 42 children, with none left over? (a) 504 (b) 54 (c) 168 (d) 84
24. 24.Two ribbons are 12 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) 3 cm (b) 12 cm (c) 1 cm (d) 9 cm
25. 25.A teacher has 24 pencils and 30 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 24 (c) 6 (d) 120
26. 26.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) 28 (d) 56
27. 27.What is the smallest number of sweets that can be shared equally among 6 children or among 15 children, with none left over? (a) 90 (b) 30 (c) 21 (d) 60
28. 28.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) 4 cm (b) 32 cm (c) 8 cm (d) 40 cm
29. 29.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) 5 min (b) 35 min (c) 250 min (d) 50 min
30. 30.Two ribbons are 21 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) 35 cm (b) 7 cm (c) 21 cm (d) 1 cm
31. 31.Two ribbons are 28 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) 2 cm (b) 28 cm (c) 4 cm (d) 224 cm
32. 32.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) 15 (b) 1 (c) 3 (d) 6
33. 33.What is the smallest number of sweets that can be shared equally among 15 children or among 25 children, with none left over? (a) 375 (b) 150 (c) 40 (d) 75
34. 34.Two ribbons are 15 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) 90 cm (b) 3 cm (c) 1 cm (d) 15 cm
35. 35.A teacher has 36 pencils and 96 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 36 (b) 12 (c) 60 (d) 6
36. 36.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) 60 min (c) 6 min (d) 42 min
37. 37.Two ribbons are 24 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) 32 cm (c) 8 cm (d) 24 cm
38. 38.Two ribbons are 40 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) 200 cm (b) 40 cm (c) 5 cm (d) 10 cm
39. 39.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) 60 (d) 120
40. 40.A teacher has 6 pencils and 14 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 8 (b) 1 (c) 6 (d) 2

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