HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 373 · 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 8 minutes and every 28 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 4 min (b) 224 min (c) 36 min (d) 56 min
2. 2.Two bells ring every 12 minutes and every 15 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 27 min (b) 180 min (c) 60 min (d) 3 min
3. 3.What is the smallest number of sweets that can be shared equally among 15 children or among 18 children, with none left over? (a) 33 (b) 270 (c) 180 (d) 90
4. 4.What is the smallest number of sweets that can be shared equally among 15 children or among 35 children, with none left over? (a) 525 (b) 50 (c) 105 (d) 210
5. 5.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) 448 (b) 8 (c) 4 (d) 56
6. 6.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) 8 cm (b) 2 cm (c) 4 cm (d) 12 cm
7. 7.A teacher has 35 pencils and 49 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) 35 (d) 7
8. 8.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) 40 cm (b) 4 cm (c) 8 cm (d) 32 cm
9. 9.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
10. 10.Two ribbons are 12 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) 12 cm (c) 4 cm (d) 20 cm
11. 11.A teacher has 45 pencils and 63 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 9 (b) 3 (c) 18 (d) 45
12. 12.What is the smallest number of sweets that can be shared equally among 20 children or among 35 children, with none left over? (a) 55 (b) 280 (c) 140 (d) 700
13. 13.What is the smallest number of sweets that can be shared equally among 12 children or among 42 children, with none left over? (a) 54 (b) 504 (c) 84 (d) 168
14. 14.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) 1 (c) 12 (d) 60
15. 15.A teacher has 12 pencils and 20 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 12 (b) 8 (c) 4 (d) 2
16. 16.What is the smallest number of sweets that can be shared equally among 6 children or among 21 children, with none left over? (a) 126 (b) 27 (c) 84 (d) 42
17. 17.A teacher has 48 pencils and 60 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 48 (c) 240 (d) 12
18. 18.A teacher has 20 pencils and 35 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 5 (b) 15 (c) 1 (d) 20
19. 19.Two ribbons are 9 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) 15 cm (b) 9 cm (c) 3 cm (d) 1 cm
20. 20.A teacher has 24 pencils and 56 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 24 (b) 32 (c) 4 (d) 8
21. 21.Two ribbons are 60 cm and 108 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 48 cm (b) 12 cm (c) 60 cm (d) 6 cm
22. 22.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) 2 min (c) 48 min (d) 24 min
23. 23.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) 16 min (b) 30 min (c) 2 min (d) 60 min
24. 24.Two bells ring every 8 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 56 min (b) 112 min (c) 22 min (d) 2 min
25. 25.A teacher has 12 pencils and 16 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 48 (b) 4 (c) 2 (d) 12
26. 26.A teacher has 8 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) 20 (c) 4 (d) 8
27. 27.A teacher has 18 pencils and 27 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 9 (c) 18 (d) 54
28. 28.Two ribbons are 24 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) 216 cm (b) 3 cm (c) 1 cm (d) 24 cm
29. 29.Two bells ring every 10 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 2 min (b) 70 min (c) 140 min (d) 24 min
30. 30.Two bells ring every 8 minutes and every 10 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 2 min (b) 40 min (c) 80 min (d) 18 min
31. 31.A teacher has 21 pencils and 56 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 21 (b) 1 (c) 35 (d) 7
32. 32.Two ribbons are 27 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) 27 cm (b) 18 cm (c) 3 cm (d) 9 cm
33. 33.What is the smallest number of sweets that can be shared equally among 12 children or among 14 children, with none left over? (a) 85 (b) 84 (c) 26 (d) 168
34. 34.A teacher has 18 pencils and 45 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 9 (b) 18 (c) 27 (d) 3
35. 35.What is the smallest number of sweets that can be shared equally among 15 children or among 20 children, with none left over? (a) 300 (b) 120 (c) 35 (d) 60
36. 36.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) 8 (c) 4 (d) 24
37. 37.Two bells ring every 20 minutes and every 35 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 55 min (b) 140 min (c) 5 min (d) 700 min
38. 38.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) 36 min (c) 216 min (d) 30 min
39. 39.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) 112 (d) 56
40. 40.Two ribbons are 12 cm and 42 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) 30 cm (d) 6 cm

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