HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 776 · 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 10 children or among 25 children, with none left over? (a) 250 (b) 100 (c) 35 (d) 50
2. 2.Two ribbons are 30 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) 30 cm (b) 180 cm (c) 6 cm (d) 3 cm
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) 63 min (c) 189 min (d) 30 min
4. 4.A teacher has 16 pencils and 40 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 16 (b) 24 (c) 8 (d) 4
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) 14 (b) 40 (c) 21 (d) 20
6. 6.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) 240 min (b) 4 min (c) 32 min (d) 60 min
7. 7.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) 28 (c) 18 (d) 29
8. 8.A teacher has 60 pencils and 72 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 360 (c) 60 (d) 12
9. 9.Two ribbons are 16 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) 1 cm (b) 16 cm (c) 144 cm (d) 2 cm
10. 10.What is the smallest number of sweets that can be shared equally among 6 children or among 15 children, with none left over? (a) 90 (b) 30 (c) 21 (d) 60
11. 11.Two ribbons are 18 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
12. 12.A teacher has 22 pencils and 77 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 22 (b) 11 (c) 55 (d) 1
13. 13.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) 378 min (c) 126 min (d) 3 min
14. 14.Two ribbons are 96 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) 6 cm (b) 12 cm (c) 96 cm (d) 864 cm
15. 15.Two ribbons are 14 cm and 49 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 7 cm (b) 1 cm (c) 14 cm (d) 35 cm
16. 16.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) 1 cm (b) 10 cm (c) 2 cm (d) 4 cm
17. 17.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) 22 min (c) 2 min (d) 60 min
18. 18.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
19. 19.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) 40 min (b) 4 min (c) 84 min (d) 336 min
20. 20.What is the smallest number of sweets that can be shared equally among 6 children or among 9 children, with none left over? (a) 36 (b) 54 (c) 18 (d) 15
21. 21.What is the smallest number of sweets that can be shared equally among 18 children or among 42 children, with none left over? (a) 60 (b) 756 (c) 126 (d) 252
22. 22.A teacher has 60 pencils and 96 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 36 (b) 6 (c) 12 (d) 60
23. 23.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) 1 cm (b) 12 cm (c) 60 cm (d) 3 cm
24. 24.Two ribbons are 44 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) 55 cm (b) 44 cm (c) 1 cm (d) 11 cm
25. 25.What is the smallest number of sweets that can be shared equally among 6 children or among 8 children, with none left over? (a) 25 (b) 48 (c) 14 (d) 24
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) 2 min (b) 40 min (c) 80 min (d) 18 min
27. 27.What is the smallest number of sweets that can be shared equally among 18 children or among 21 children, with none left over? (a) 252 (b) 126 (c) 378 (d) 39
28. 28.What is the smallest number of sweets that can be shared equally among 10 children or among 14 children, with none left over? (a) 70 (b) 71 (c) 140 (d) 24
29. 29.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) 48 (c) 4 (d) 8
30. 30.Two ribbons are 49 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) 49 cm (b) 14 cm (c) 7 cm (d) 1 cm
31. 31.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) 105 min (b) 315 min (c) 3 min (d) 36 min
32. 32.What is the smallest number of sweets that can be shared equally among 25 children or among 30 children, with none left over? (a) 55 (b) 300 (c) 750 (d) 150
33. 33.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) 48 min (b) 24 min (c) 2 min (d) 14 min
34. 34.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) 2 min (b) 20 min (c) 40 min (d) 14 min
35. 35.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
36. 36.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) 112 (d) 44
37. 37.A teacher has 18 pencils and 48 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 18 (b) 6 (c) 30 (d) 3
38. 38.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) 26 (c) 168 (d) 84
39. 39.What is the smallest number of sweets that can be shared equally among 10 children or among 15 children, with none left over? (a) 60 (b) 150 (c) 25 (d) 30
40. 40.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) 3 min (c) 36 min (d) 108 min

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