HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 583 · 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 30 cm and 70 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) 5 cm (c) 40 cm (d) 10 cm
2. 2.Two ribbons are 32 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) 32 cm (b) 288 cm (c) 4 cm (d) 2 cm
3. 3.What is the smallest number of sweets that can be shared equally among 8 children or among 14 children, with none left over? (a) 22 (b) 56 (c) 57 (d) 112
4. 4.What is the smallest number of sweets that can be shared equally among 10 children or among 15 children, with none left over? (a) 150 (b) 30 (c) 25 (d) 60
5. 5.What is the smallest number of sweets that can be shared equally among 4 children or among 6 children, with none left over? (a) 13 (b) 10 (c) 24 (d) 12
6. 6.Two bells ring every 9 minutes and every 12 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 108 min (b) 3 min (c) 21 min (d) 36 min
7. 7.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) 15 cm (b) 1 cm (c) 3 cm (d) 12 cm
8. 8.Two ribbons are 16 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) 4 cm (b) 16 cm (c) 2 cm (d) 20 cm
9. 9.What is the smallest number of sweets that can be shared equally among 6 children or among 10 children, with none left over? (a) 60 (b) 31 (c) 16 (d) 30
10. 10.Two ribbons are 15 cm and 20 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) 1 cm (c) 15 cm (d) 60 cm
11. 11.A teacher has 50 pencils and 90 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 40 (b) 50 (c) 10 (d) 5
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.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) 250 min (b) 50 min (c) 35 min (d) 5 min
14. 14.Two ribbons are 20 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) 15 cm (b) 1 cm (c) 5 cm (d) 20 cm
15. 15.A teacher has 36 pencils and 48 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 144 (b) 36 (c) 12 (d) 6
16. 16.What is the smallest number of sweets that can be shared equally among 24 children or among 30 children, with none left over? (a) 720 (b) 240 (c) 120 (d) 54
17. 17.Two ribbons are 14 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) 49 cm (b) 7 cm (c) 14 cm (d) 1 cm
18. 18.Two ribbons are 6 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) 1 cm (b) 15 cm (c) 6 cm (d) 3 cm
19. 19.Two ribbons are 25 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) 25 cm (b) 20 cm (c) 5 cm (d) 1 cm
20. 20.What is the smallest number of sweets that can be shared equally among 12 children or among 15 children, with none left over? (a) 27 (b) 120 (c) 180 (d) 60
21. 21.Two ribbons are 22 cm and 99 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 11 cm (b) 77 cm (c) 1 cm (d) 22 cm
22. 22.Two ribbons are 6 cm and 16 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) 6 cm (c) 10 cm (d) 2 cm
23. 23.A teacher has 49 pencils and 63 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) 49
24. 24.A teacher has 21 pencils and 27 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 21 (b) 3 (c) 6 (d) 1
25. 25.Two ribbons are 22 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) 22 cm (c) 11 cm (d) 33 cm
26. 26.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
27. 27.A teacher has 96 pencils and 108 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 864 (b) 6 (c) 96 (d) 12
28. 28.A teacher has 16 pencils and 20 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 80 (b) 2 (c) 4 (d) 16
29. 29.Two ribbons are 24 cm and 64 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 40 cm (b) 4 cm (c) 24 cm (d) 8 cm
30. 30.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) 7 cm (b) 49 cm (c) 1 cm (d) 14 cm
31. 31.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) 60 min (b) 120 min (c) 22 min (d) 2 min
32. 32.A teacher has 6 pencils and 16 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 2 (c) 10 (d) 1
33. 33.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) 84 min (b) 2 min (c) 20 min (d) 42 min
34. 34.Two ribbons are 21 cm and 49 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) 28 cm (c) 1 cm (d) 7 cm
35. 35.Two ribbons are 35 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) 28 cm (c) 1 cm (d) 7 cm
36. 36.What is the smallest number of sweets that can be shared equally among 6 children or among 8 children, with none left over? (a) 25 (b) 24 (c) 48 (d) 14
37. 37.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) 4 (b) 2 (c) 1 (d) 6
38. 38.Two bells ring every 6 minutes and every 15 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 3 min (b) 30 min (c) 21 min (d) 90 min
39. 39.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) 30 (b) 5 (c) 120 (d) 10
40. 40.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) 30 min (c) 5 min (d) 25 min

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