HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 31 · 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 12 minutes and every 18 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 216 min (b) 6 min (c) 36 min (d) 30 min
2. 2.Two ribbons are 8 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) 40 cm (b) 2 cm (c) 1 cm (d) 8 cm
3. 3.A teacher has 8 pencils and 12 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 2 (b) 4 (c) 24 (d) 8
4. 4.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
5. 5.Two bells ring every 9 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 189 min (b) 3 min (c) 30 min (d) 63 min
6. 6.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) 1 cm (b) 11 cm (c) 22 cm (d) 77 cm
7. 7.Two ribbons are 12 cm and 15 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 60 cm (b) 12 cm (c) 3 cm (d) 1 cm
8. 8.Two bells ring every 18 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 39 min (b) 126 min (c) 3 min (d) 378 min
9. 9.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
10. 10.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) 1 (c) 5 (d) 15
11. 11.What is the smallest number of sweets that can be shared equally among 9 children or among 12 children, with none left over? (a) 21 (b) 108 (c) 36 (d) 72
12. 12.Two bells ring every 12 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 168 min (b) 84 min (c) 26 min (d) 2 min
13. 13.What is the smallest number of sweets that can be shared equally among 6 children or among 15 children, with none left over? (a) 60 (b) 30 (c) 21 (d) 90
14. 14.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) 2 min (b) 84 min (c) 20 min (d) 42 min
15. 15.Two ribbons are 21 cm and 28 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) 21 cm (c) 7 cm (d) 84 cm
16. 16.A teacher has 48 pencils and 108 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 48 (b) 6 (c) 60 (d) 12
17. 17.Two bells ring every 15 minutes and every 20 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 60 min (b) 35 min (c) 300 min (d) 5 min
18. 18.A teacher has 48 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) 36 (c) 48 (d) 12
19. 19.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) 6 min (b) 360 min (c) 42 min (d) 60 min
20. 20.A teacher has 8 pencils and 10 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 40 (b) 1 (c) 8 (d) 2
21. 21.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) 60 (b) 1 (c) 3 (d) 12
22. 22.What is the smallest number of sweets that can be shared equally among 16 children or among 28 children, with none left over? (a) 224 (b) 448 (c) 44 (d) 112
23. 23.A teacher has 24 pencils and 32 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 4 (b) 96 (c) 8 (d) 24
24. 24.What is the smallest number of sweets that can be shared equally among 9 children or among 21 children, with none left over? (a) 189 (b) 30 (c) 63 (d) 126
25. 25.What is the smallest number of sweets that can be shared equally among 12 children or among 30 children, with none left over? (a) 42 (b) 60 (c) 120 (d) 360
26. 26.Two ribbons are 6 cm and 15 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) 9 cm (c) 3 cm (d) 1 cm
27. 27.A teacher has 14 pencils and 21 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 14 (b) 1 (c) 42 (d) 7
28. 28.A teacher has 28 pencils and 36 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 4 (b) 8 (c) 2 (d) 28
29. 29.A teacher has 24 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) 40 (c) 8 (d) 24
30. 30.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) 6 min (c) 84 min (d) 54 min
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) 2 min (c) 22 min (d) 120 min
32. 32.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) 50 (c) 10 (d) 30
33. 33.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) 6 (b) 2 (c) 1 (d) 8
34. 34.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) 756 min (b) 126 min (c) 6 min (d) 60 min
35. 35.A teacher has 35 pencils and 63 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) 7 (d) 28
36. 36.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) 4 min (b) 336 min (c) 84 min (d) 40 min
37. 37.What is the smallest number of sweets that can be shared equally among 8 children or among 28 children, with none left over? (a) 224 (b) 36 (c) 56 (d) 112
38. 38.A teacher has 12 pencils and 27 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 12 (b) 1 (c) 3 (d) 15
39. 39.A teacher has 30 pencils and 48 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 18 (c) 3 (d) 30
40. 40.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) 100 min (b) 45 min (c) 5 min (d) 500 min

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