HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 334 · 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.A teacher has 40 pencils and 50 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) 200 (d) 40
2. 2.Two bells ring every 4 minutes and every 10 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 40 min (b) 2 min (c) 20 min (d) 14 min
3. 3.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) 3 min (b) 30 min (c) 189 min (d) 63 min
4. 4.A teacher has 16 pencils and 24 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 4 (b) 16 (c) 48 (d) 8
5. 5.What is the smallest number of sweets that can be shared equally among 4 children or among 10 children, with none left over? (a) 20 (b) 21 (c) 40 (d) 14
6. 6.Two ribbons are 6 cm and 9 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) 18 cm (c) 3 cm (d) 1 cm
7. 7.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) 2 min (b) 60 min (c) 22 min (d) 120 min
8. 8.Two ribbons are 12 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) 2 cm (b) 4 cm (c) 48 cm (d) 12 cm
9. 9.Two ribbons are 40 cm and 90 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) 40 cm (c) 10 cm (d) 50 cm
10. 10.Two ribbons are 12 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) 12 cm (c) 3 cm (d) 9 cm
11. 11.Two ribbons are 60 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) 5 cm (b) 60 cm (c) 420 cm (d) 10 cm
12. 12.Two bells ring every 12 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 33 min (b) 3 min (c) 252 min (d) 84 min
13. 13.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) 25 min (b) 5 min (c) 30 min (d) 150 min
14. 14.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) 2 min (c) 56 min (d) 28 min
15. 15.A teacher has 14 pencils and 49 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 14 (c) 35 (d) 7
16. 16.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) 60 (b) 12 (c) 6 (d) 24
17. 17.Two ribbons are 4 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) 4 cm (b) 1 cm (c) 10 cm (d) 2 cm
18. 18.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) 21 min (b) 36 min (c) 108 min (d) 3 min
19. 19.What is the smallest number of sweets that can be shared equally among 8 children or among 10 children, with none left over? (a) 18 (b) 41 (c) 80 (d) 40
20. 20.What is the smallest number of sweets that can be shared equally among 12 children or among 16 children, with none left over? (a) 48 (b) 192 (c) 28 (d) 96
21. 21.A teacher has 15 pencils and 35 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 20 (c) 5 (d) 15
22. 22.What is the smallest number of sweets that can be shared equally among 20 children or among 25 children, with none left over? (a) 500 (b) 100 (c) 45 (d) 200
23. 23.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) 18 min (d) 3 min
24. 24.What is the smallest number of sweets that can be shared equally among 12 children or among 14 children, with none left over? (a) 84 (b) 168 (c) 26 (d) 85
25. 25.A teacher has 30 pencils and 35 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 30 (b) 1 (c) 5 (d) 210
26. 26.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) 18 min (b) 2 min (c) 40 min (d) 80 min
27. 27.Two ribbons are 55 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) 55 cm (b) 22 cm (c) 11 cm (d) 1 cm
28. 28.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) 4 cm (c) 96 cm (d) 24 cm
29. 29.What is the smallest number of sweets that can be shared equally among 12 children or among 18 children, with none left over? (a) 216 (b) 30 (c) 36 (d) 72
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) 84 min (b) 504 min (c) 54 min (d) 6 min
31. 31.Two ribbons are 33 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
32. 32.What is the smallest number of sweets that can be shared equally among 12 children or among 28 children, with none left over? (a) 336 (b) 168 (c) 84 (d) 40
33. 33.A teacher has 24 pencils and 108 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 24 (b) 84 (c) 6 (d) 12
34. 34.What is the smallest number of sweets that can be shared equally among 15 children or among 21 children, with none left over? (a) 315 (b) 105 (c) 36 (d) 210
35. 35.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) 16 cm (b) 4 cm (c) 8 cm (d) 24 cm
36. 36.Two bells ring every 4 minutes and every 6 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 24 min (b) 12 min (c) 2 min (d) 10 min
37. 37.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) 112 min (b) 22 min (c) 2 min (d) 56 min
38. 38.What is the smallest number of sweets that can be shared equally among 20 children or among 24 children, with none left over? (a) 480 (b) 120 (c) 240 (d) 44
39. 39.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) 36 min (b) 30 min (c) 6 min (d) 216 min
40. 40.What is the smallest number of sweets that can be shared equally among 24 children or among 30 children, with none left over? (a) 240 (b) 720 (c) 54 (d) 120

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