HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 999 · 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 18 minutes and every 30 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 48 min (b) 90 min (c) 540 min (d) 6 min
2. 2.Two bells ring every 8 minutes and every 20 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 4 min (b) 160 min (c) 40 min (d) 28 min
3. 3.Two bells ring every 8 minutes and every 12 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 20 min (b) 4 min (c) 24 min (d) 96 min
4. 4.A teacher has 24 pencils and 28 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 4 (b) 2 (c) 168 (d) 24
5. 5.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
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) 80 min (b) 36 min (c) 320 min (d) 4 min
7. 7.What is the smallest number of sweets that can be shared equally among 9 children or among 21 children, with none left over? (a) 126 (b) 63 (c) 189 (d) 30
8. 8.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
9. 9.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) 39 (c) 252 (d) 126
10. 10.What is the smallest number of sweets that can be shared equally among 10 children or among 15 children, with none left over? (a) 150 (b) 30 (c) 60 (d) 25
11. 11.A teacher has 12 pencils and 20 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 12 (b) 8 (c) 4 (d) 2
12. 12.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) 22 (c) 112 (d) 56
13. 13.Two ribbons are 48 cm and 54 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 432 cm (b) 48 cm (c) 6 cm (d) 3 cm
14. 14.A teacher has 20 pencils and 28 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 2 (b) 20 (c) 8 (d) 4
15. 15.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) 4 cm (d) 2 cm
16. 16.A teacher has 6 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) 6 (c) 10 (d) 2
17. 17.What is the smallest number of sweets that can be shared equally among 15 children or among 35 children, with none left over? (a) 525 (b) 105 (c) 50 (d) 210
18. 18.A teacher has 35 pencils and 63 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 7 (c) 35 (d) 28
19. 19.A teacher has 64 pencils and 72 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 4 (b) 576 (c) 8 (d) 64
20. 20.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) 24 (b) 12 (c) 60 (d) 6
21. 21.What is the smallest number of sweets that can be shared equally among 16 children or among 20 children, with none left over? (a) 320 (b) 80 (c) 36 (d) 160
22. 22.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) 42 min (b) 6 min (c) 360 min (d) 60 min
23. 23.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) 2 (b) 6 (c) 1 (d) 4
24. 24.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) 6 min (d) 84 min
25. 25.What is the smallest number of sweets that can be shared equally among 20 children or among 35 children, with none left over? (a) 55 (b) 280 (c) 700 (d) 140
26. 26.What is the smallest number of sweets that can be shared equally among 6 children or among 15 children, with none left over? (a) 21 (b) 60 (c) 90 (d) 30
27. 27.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
28. 28.Two ribbons are 24 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) 84 cm (b) 24 cm (c) 6 cm (d) 12 cm
29. 29.Two bells ring every 6 minutes and every 10 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 2 min (b) 60 min (c) 16 min (d) 30 min
30. 30.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) 300 min (b) 35 min (c) 60 min (d) 5 min
31. 31.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) 36 min (b) 56 min (c) 224 min (d) 4 min
32. 32.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) 3 min (b) 21 min (c) 36 min (d) 108 min
33. 33.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) 240 (c) 44 (d) 120
34. 34.A teacher has 12 pencils and 15 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 3 (c) 12 (d) 60
35. 35.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) 100 min (b) 500 min (c) 5 min (d) 45 min
36. 36.A teacher has 36 pencils and 42 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 36 (b) 3 (c) 6 (d) 252
37. 37.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) 2 cm (b) 4 cm (c) 12 cm (d) 8 cm
38. 38.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
39. 39.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) 90 min (b) 270 min (c) 33 min (d) 3 min
40. 40.Two ribbons are 12 cm and 27 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) 3 cm (c) 12 cm (d) 15 cm

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