HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 642 · 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 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) 14 cm (b) 1 cm (c) 7 cm (d) 49 cm
2. 2.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) 28 min (c) 56 min (d) 2 min
3. 3.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) 2 cm (b) 1 cm (c) 8 cm (d) 6 cm
4. 4.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) 20 (b) 4 (c) 120 (d) 2
5. 5.A teacher has 70 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) 70 (c) 560 (d) 10
6. 6.What is the smallest number of sweets that can be shared equally among 8 children or among 20 children, with none left over? (a) 80 (b) 40 (c) 160 (d) 28
7. 7.A teacher has 10 pencils and 45 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) 35 (d) 1
8. 8.Two ribbons are 16 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) 56 cm (c) 8 cm (d) 16 cm
9. 9.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) 40 min (b) 84 min (c) 336 min (d) 4 min
10. 10.Two ribbons are 24 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) 24 cm (c) 60 cm (d) 12 cm
11. 11.Two ribbons are 16 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) 8 cm (b) 4 cm (c) 16 cm (d) 40 cm
12. 12.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
13. 13.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
14. 14.A teacher has 20 pencils and 30 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 60 (b) 10 (c) 20 (d) 5
15. 15.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) 1 (b) 35 (c) 5 (d) 10
16. 16.What is the smallest number of sweets that can be shared equally among 6 children or among 15 children, with none left over? (a) 30 (b) 90 (c) 21 (d) 60
17. 17.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) 60 (c) 35 (d) 300
18. 18.Two ribbons are 15 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) 1 cm (b) 25 cm (c) 5 cm (d) 15 cm
19. 19.A teacher has 9 pencils and 12 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 9 (c) 36 (d) 3
20. 20.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) 42 min (b) 27 min (c) 3 min (d) 126 min
21. 21.Two ribbons are 44 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) 33 cm (b) 11 cm (c) 44 cm (d) 1 cm
22. 22.A teacher has 24 pencils and 84 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) 24 (d) 60
23. 23.Two ribbons are 12 cm and 30 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) 18 cm (c) 6 cm (d) 12 cm
24. 24.Two ribbons are 24 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) 8 cm (b) 24 cm (c) 96 cm (d) 4 cm
25. 25.Two ribbons are 4 cm and 10 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) 4 cm (d) 6 cm
26. 26.Two ribbons are 36 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) 9 cm (b) 3 cm (c) 27 cm (d) 36 cm
27. 27.Two ribbons are 15 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) 1 cm (b) 15 cm (c) 9 cm (d) 3 cm
28. 28.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
29. 29.What is the smallest number of sweets that can be shared equally among 10 children or among 25 children, with none left over? (a) 50 (b) 35 (c) 100 (d) 250
30. 30.Two ribbons are 21 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) 21 cm (b) 1 cm (c) 168 cm (d) 3 cm
31. 31.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) 20 cm (b) 5 cm (c) 15 cm (d) 1 cm
32. 32.A teacher has 12 pencils and 15 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 60 (c) 1 (d) 12
33. 33.Two bells ring every 8 minutes and every 12 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 24 min (b) 20 min (c) 96 min (d) 4 min
34. 34.Two ribbons are 12 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) 3 cm (b) 36 cm (c) 12 cm (d) 6 cm
35. 35.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) 48 min (b) 2 min (c) 14 min (d) 24 min
36. 36.Two ribbons are 49 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) 49 cm (b) 1 cm (c) 392 cm (d) 7 cm
37. 37.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) 30 min (c) 216 min (d) 36 min
38. 38.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) 18 min (b) 15 min (c) 54 min (d) 3 min
39. 39.What is the smallest number of sweets that can be shared equally among 12 children or among 16 children, with none left over? (a) 96 (b) 28 (c) 192 (d) 48
40. 40.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

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