HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 982 · 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 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) 24 min (b) 14 min (c) 2 min (d) 48 min
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) 2 min (b) 18 min (c) 56 min (d) 28 min
3. 3.A teacher has 20 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) 5 (c) 20 (d) 25
4. 4.Two ribbons are 20 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) 20 cm (b) 5 cm (c) 30 cm (d) 10 cm
5. 5.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) 54 min (b) 15 min (c) 3 min (d) 18 min
6. 6.A teacher has 32 pencils and 72 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 32 (b) 4 (c) 8 (d) 40
7. 7.Two ribbons are 30 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) 10 cm (b) 30 cm (c) 5 cm (d) 50 cm
8. 8.Two ribbons are 8 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) 2 cm (b) 8 cm (c) 4 cm (d) 12 cm
9. 9.Two bells ring every 24 minutes and every 30 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 720 min (b) 54 min (c) 120 min (d) 6 min
10. 10.Two ribbons are 16 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) 16 cm (c) 4 cm (d) 8 cm
11. 11.What is the smallest number of sweets that can be shared equally among 15 children or among 25 children, with none left over? (a) 40 (b) 150 (c) 75 (d) 375
12. 12.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) 32 (b) 4 (c) 8 (d) 24
13. 13.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) 21 cm (b) 3 cm (c) 6 cm (d) 1 cm
14. 14.A teacher has 10 pencils and 25 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) 15
15. 15.A teacher has 50 pencils and 60 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 300 (b) 50 (c) 10 (d) 5
16. 16.A teacher has 42 pencils and 54 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 42 (c) 12 (d) 6
17. 17.What is the smallest number of sweets that can be shared equally among 6 children or among 14 children, with none left over? (a) 20 (b) 42 (c) 43 (d) 84
18. 18.What is the smallest number of sweets that can be shared equally among 4 children or among 14 children, with none left over? (a) 56 (b) 18 (c) 29 (d) 28
19. 19.What is the smallest number of sweets that can be shared equally among 12 children or among 42 children, with none left over? (a) 168 (b) 504 (c) 54 (d) 84
20. 20.A teacher has 15 pencils and 25 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 15 (c) 5 (d) 10
21. 21.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) 16 (c) 4 (d) 12
22. 22.What is the smallest number of sweets that can be shared equally among 25 children or among 30 children, with none left over? (a) 750 (b) 300 (c) 55 (d) 150
23. 23.Two ribbons are 6 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) 4 cm (b) 6 cm (c) 1 cm (d) 2 cm
24. 24.A teacher has 27 pencils and 45 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 18 (b) 27 (c) 9 (d) 3
25. 25.What is the smallest number of sweets that can be shared equally among 15 children or among 18 children, with none left over? (a) 270 (b) 180 (c) 90 (d) 33
26. 26.Two bells ring every 15 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 36 min (b) 105 min (c) 3 min (d) 315 min
27. 27.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) 5 (c) 50 (d) 10
28. 28.Two ribbons are 27 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) 108 cm (b) 9 cm (c) 3 cm (d) 27 cm
29. 29.A teacher has 40 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) 5 (d) 10
30. 30.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) 480 min (b) 44 min (c) 4 min (d) 120 min
31. 31.A teacher has 84 pencils and 108 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) 84
32. 32.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) 36 (b) 3 (c) 1 (d) 9
33. 33.What is the smallest number of sweets that can be shared equally among 6 children or among 9 children, with none left over? (a) 15 (b) 18 (c) 54 (d) 36
34. 34.What is the smallest number of sweets that can be shared equally among 6 children or among 21 children, with none left over? (a) 84 (b) 27 (c) 42 (d) 126
35. 35.Two ribbons are 18 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) 18 cm (c) 126 cm (d) 3 cm
36. 36.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) 6 min (b) 126 min (c) 60 min (d) 756 min
37. 37.A teacher has 40 pencils and 70 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 40 (b) 10 (c) 30 (d) 5
38. 38.A teacher has 55 pencils and 77 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 55 (b) 1 (c) 11 (d) 22
39. 39.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) 36 (c) 210 (d) 315
40. 40.Two ribbons are 24 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) 24 cm (b) 3 cm (c) 120 cm (d) 6 cm

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