HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 271 · 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.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) 84 (c) 168 (d) 504
2. 2.What is the smallest number of sweets that can be shared equally among 10 children or among 15 children, with none left over? (a) 25 (b) 60 (c) 150 (d) 30
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) 270 (b) 33 (c) 90 (d) 180
4. 4.Two ribbons are 35 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) 35 cm (c) 280 cm (d) 5 cm
5. 5.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) 120 min (b) 480 min (c) 4 min (d) 44 min
6. 6.Two ribbons are 20 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) 70 cm (b) 5 cm (c) 20 cm (d) 10 cm
7. 7.Two ribbons are 77 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) 77 cm (b) 1 cm (c) 11 cm (d) 22 cm
8. 8.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) 8 (b) 24 (c) 32 (d) 4
9. 9.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) 21 (c) 90 (d) 30
10. 10.A teacher has 60 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) 12 (d) 60
11. 11.A teacher has 20 pencils and 32 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 2 (b) 12 (c) 20 (d) 4
12. 12.Two ribbons are 10 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) 2 cm (b) 1 cm (c) 8 cm (d) 10 cm
13. 13.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) 14 min (c) 20 min (d) 2 min
14. 14.A teacher has 45 pencils and 72 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 45 (b) 9 (c) 27 (d) 3
15. 15.Two bells ring every 15 minutes and every 35 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 50 min (b) 525 min (c) 105 min (d) 5 min
16. 16.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) 6 min (c) 504 min (d) 54 min
17. 17.A teacher has 8 pencils and 18 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 2 (b) 10 (c) 8 (d) 1
18. 18.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) 35 (b) 10 (c) 5 (d) 1
19. 19.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
20. 20.What is the smallest number of sweets that can be shared equally among 12 children or among 18 children, with none left over? (a) 36 (b) 30 (c) 72 (d) 216
21. 21.What is the smallest number of sweets that can be shared equally among 10 children or among 35 children, with none left over? (a) 140 (b) 45 (c) 70 (d) 350
22. 22.Two ribbons are 45 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) 3 cm (b) 18 cm (c) 9 cm (d) 45 cm
23. 23.A teacher has 10 pencils and 14 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 2 (b) 1 (c) 10 (d) 4
24. 24.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) 60 min (c) 360 min (d) 42 min
25. 25.A teacher has 35 pencils and 56 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 35 (b) 7 (c) 21 (d) 1
26. 26.A teacher has 33 pencils and 88 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 55 (c) 11 (d) 33
27. 27.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) 336 min (b) 4 min (c) 40 min (d) 84 min
28. 28.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) 1 cm (b) 5 cm (c) 20 cm (d) 15 cm
29. 29.Two bells ring every 15 minutes and every 18 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 33 min (b) 90 min (c) 270 min (d) 3 min
30. 30.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) 16 (b) 4 (c) 8 (d) 48
31. 31.A teacher has 6 pencils and 10 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 6 (c) 2 (d) 4
32. 32.Two ribbons are 10 cm and 12 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) 60 cm (c) 10 cm (d) 2 cm
33. 33.Two bells ring every 16 minutes and every 28 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 4 min (b) 448 min (c) 44 min (d) 112 min
34. 34.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) 2 min (c) 112 min (d) 22 min
35. 35.Two bells ring every 9 minutes and every 15 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 45 min (b) 24 min (c) 135 min (d) 3 min
36. 36.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) 120 min (b) 2 min (c) 60 min (d) 22 min
37. 37.A teacher has 24 pencils and 54 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 24 (b) 30 (c) 6 (d) 3
38. 38.What is the smallest number of sweets that can be shared equally among 15 children or among 21 children, with none left over? (a) 36 (b) 315 (c) 105 (d) 210
39. 39.What is the smallest number of sweets that can be shared equally among 8 children or among 12 children, with none left over? (a) 48 (b) 96 (c) 20 (d) 24
40. 40.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) 5 cm (b) 10 cm (c) 30 cm (d) 50 cm

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