HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 142 · 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 18 children or among 21 children, with none left over? (a) 378 (b) 252 (c) 39 (d) 126
2. 2.Two bells ring every 12 minutes and every 16 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 192 min (b) 28 min (c) 48 min (d) 4 min
3. 3.Two ribbons are 18 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) 18 cm (b) 24 cm (c) 6 cm (d) 3 cm
4. 4.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) 12 cm (b) 1 cm (c) 60 cm (d) 3 cm
5. 5.Two bells ring every 25 minutes and every 30 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 750 min (b) 5 min (c) 150 min (d) 55 min
6. 6.A teacher has 10 pencils and 16 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 2 (c) 10 (d) 6
7. 7.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) 30 cm (b) 12 cm (c) 3 cm (d) 6 cm
8. 8.A teacher has 25 pencils and 45 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 25 (b) 20 (c) 5 (d) 1
9. 9.What is the smallest number of sweets that can be shared equally among 8 children or among 10 children, with none left over? (a) 80 (b) 18 (c) 41 (d) 40
10. 10.Two ribbons are 12 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) 12 cm (b) 2 cm (c) 4 cm (d) 8 cm
11. 11.A teacher has 50 pencils and 90 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 10 (b) 50 (c) 5 (d) 40
12. 12.What is the smallest number of sweets that can be shared equally among 12 children or among 20 children, with none left over? (a) 120 (b) 240 (c) 32 (d) 60
13. 13.Two ribbons are 28 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) 28 cm (b) 140 cm (c) 1 cm (d) 7 cm
14. 14.What is the smallest number of sweets that can be shared equally among 8 children or among 14 children, with none left over? (a) 57 (b) 56 (c) 112 (d) 22
15. 15.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) 2 min (b) 28 min (c) 18 min (d) 56 min
16. 16.What is the smallest number of sweets that can be shared equally among 8 children or among 12 children, with none left over? (a) 20 (b) 24 (c) 96 (d) 48
17. 17.What is the smallest number of sweets that can be shared equally among 20 children or among 35 children, with none left over? (a) 700 (b) 55 (c) 280 (d) 140
18. 18.What is the smallest number of sweets that can be shared equally among 9 children or among 12 children, with none left over? (a) 72 (b) 21 (c) 36 (d) 108
19. 19.What is the smallest number of sweets that can be shared equally among 12 children or among 14 children, with none left over? (a) 168 (b) 26 (c) 84 (d) 85
20. 20.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) 54 min (c) 84 min (d) 6 min
21. 21.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) 12 min (b) 2 min (c) 10 min (d) 24 min
22. 22.Two ribbons are 28 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) 2 cm (b) 8 cm (c) 28 cm (d) 4 cm
23. 23.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) 29 (c) 28 (d) 18
24. 24.Two ribbons are 12 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) 12 cm (b) 84 cm (c) 2 cm (d) 1 cm
25. 25.Two ribbons are 20 cm and 30 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) 5 cm (c) 20 cm (d) 10 cm
26. 26.Two ribbons are 12 cm and 30 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 12 cm (b) 6 cm (c) 18 cm (d) 3 cm
27. 27.Two ribbons are 27 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) 9 cm (b) 36 cm (c) 27 cm (d) 3 cm
28. 28.What is the smallest number of sweets that can be shared equally among 12 children or among 15 children, with none left over? (a) 180 (b) 120 (c) 60 (d) 27
29. 29.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) 525 min (b) 105 min (c) 50 min (d) 5 min
30. 30.A teacher has 30 pencils and 42 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 30 (b) 6 (c) 3 (d) 12
31. 31.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) 4 (b) 12 (c) 2 (d) 20
32. 32.Two bells ring every 10 minutes and every 25 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 35 min (b) 5 min (c) 250 min (d) 50 min
33. 33.What is the smallest number of sweets that can be shared equally among 25 children or among 30 children, with none left over? (a) 750 (b) 300 (c) 55 (d) 150
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) 60 min (c) 126 min (d) 6 min
35. 35.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) 24 min (b) 2 min (c) 14 min (d) 48 min
36. 36.Two bells ring every 15 minutes and every 25 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 75 min (b) 5 min (c) 40 min (d) 375 min
37. 37.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) 500 min (b) 45 min (c) 5 min (d) 100 min
38. 38.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) 168 (c) 504 (d) 84
39. 39.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) 14 min (c) 20 min (d) 40 min
40. 40.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) 180 (c) 90 (d) 270

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