HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 846 · 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 12 minutes and every 15 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 3 min (b) 180 min (c) 27 min (d) 60 min
2. 2.A teacher has 48 pencils and 84 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) 36
3. 3.A teacher has 30 pencils and 40 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 120 (b) 30 (c) 10 (d) 5
4. 4.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) 224 min (b) 56 min (c) 4 min (d) 36 min
5. 5.A teacher has 24 pencils and 42 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 18 (c) 24 (d) 6
6. 6.Two bells ring every 16 minutes and every 20 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 320 min (b) 4 min (c) 80 min (d) 36 min
7. 7.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) 448 min (b) 44 min (c) 112 min (d) 4 min
8. 8.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) 3 min (c) 15 min (d) 18 min
9. 9.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) 60 min (b) 360 min (c) 6 min (d) 42 min
10. 10.What is the smallest number of sweets that can be shared equally among 20 children or among 25 children, with none left over? (a) 45 (b) 200 (c) 100 (d) 500
11. 11.What is the smallest number of sweets that can be shared equally among 6 children or among 21 children, with none left over? (a) 27 (b) 126 (c) 42 (d) 84
12. 12.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) 1 (b) 4 (c) 2 (d) 10
13. 13.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) 5 min (b) 500 min (c) 45 min (d) 100 min
14. 14.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) 6 (b) 36 (c) 12 (d) 60
15. 15.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
16. 16.Two ribbons are 22 cm and 33 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) 66 cm (c) 22 cm (d) 11 cm
17. 17.What is the smallest number of sweets that can be shared equally among 6 children or among 14 children, with none left over? (a) 43 (b) 20 (c) 84 (d) 42
18. 18.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) 168 (d) 84
19. 19.Two ribbons are 16 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) 16 cm (b) 4 cm (c) 8 cm (d) 56 cm
20. 20.A teacher has 24 pencils and 64 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) 40 (d) 4
21. 21.A teacher has 22 pencils and 55 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 11 (b) 33 (c) 1 (d) 22
22. 22.What is the smallest number of sweets that can be shared equally among 9 children or among 15 children, with none left over? (a) 45 (b) 24 (c) 135 (d) 90
23. 23.Two bells ring every 24 minutes and every 30 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 54 min (b) 720 min (c) 120 min (d) 6 min
24. 24.What is the smallest number of sweets that can be shared equally among 8 children or among 28 children, with none left over? (a) 112 (b) 224 (c) 56 (d) 36
25. 25.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) 80 min (b) 40 min (c) 18 min (d) 2 min
26. 26.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) 4 min (b) 44 min (c) 480 min (d) 120 min
27. 27.Two ribbons are 25 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) 150 cm (b) 1 cm (c) 5 cm (d) 25 cm
28. 28.Two ribbons are 40 cm and 64 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 24 cm (b) 8 cm (c) 4 cm (d) 40 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) 270 min (c) 90 min (d) 3 min
30. 30.A teacher has 28 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) 4 (c) 224 (d) 28
31. 31.What is the smallest number of sweets that can be shared equally among 12 children or among 21 children, with none left over? (a) 33 (b) 252 (c) 168 (d) 84
32. 32.Two ribbons are 44 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) 44 cm (b) 1 cm (c) 11 cm (d) 33 cm
33. 33.Two bells ring every 15 minutes and every 20 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 5 min (b) 300 min (c) 60 min (d) 35 min
34. 34.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) 55 (c) 150 (d) 300
35. 35.A teacher has 48 pencils and 108 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 60 (c) 48 (d) 12
36. 36.What is the smallest number of sweets that can be shared equally among 9 children or among 21 children, with none left over? (a) 30 (b) 189 (c) 126 (d) 63
37. 37.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) 22 cm (b) 11 cm (c) 1 cm (d) 55 cm
38. 38.Two ribbons are 22 cm and 55 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) 1 cm (c) 11 cm (d) 22 cm
39. 39.What is the smallest number of sweets that can be shared equally among 20 children or among 28 children, with none left over? (a) 280 (b) 140 (c) 48 (d) 560
40. 40.Two ribbons are 15 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) 25 cm (b) 15 cm (c) 5 cm (d) 1 cm

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