HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 622 · 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 25 children or among 30 children, with none left over? (a) 300 (b) 750 (c) 55 (d) 150
2. 2.A teacher has 21 pencils and 24 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 1 (c) 21 (d) 168
3. 3.Two bells ring every 10 minutes and every 15 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 25 min (b) 150 min (c) 5 min (d) 30 min
4. 4.What is the smallest number of sweets that can be shared equally among 10 children or among 14 children, with none left over? (a) 24 (b) 70 (c) 140 (d) 71
5. 5.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) 6 min (b) 54 min (c) 504 min (d) 84 min
6. 6.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) 270 min (b) 33 min (c) 90 min (d) 3 min
7. 7.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) 5 min (b) 250 min (c) 50 min (d) 35 min
8. 8.A teacher has 15 pencils and 40 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 15 (b) 1 (c) 25 (d) 5
9. 9.Two ribbons are 49 cm and 56 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) 49 cm (c) 1 cm (d) 392 cm
10. 10.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) 108 min (d) 36 min
11. 11.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) 22 min (b) 112 min (c) 56 min (d) 2 min
12. 12.A teacher has 6 pencils and 8 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 24 (c) 2 (d) 1
13. 13.Two ribbons are 40 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) 5 cm (b) 50 cm (c) 10 cm (d) 40 cm
14. 14.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) 24 min (b) 2 min (c) 12 min (d) 10 min
15. 15.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
16. 16.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) 41 (c) 40 (d) 18
17. 17.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) 5 cm (b) 150 cm (c) 25 cm (d) 1 cm
18. 18.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) 30 min (c) 16 min (d) 60 min
19. 19.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) 18 min (c) 56 min (d) 28 min
20. 20.What is the smallest number of sweets that can be shared equally among 10 children or among 12 children, with none left over? (a) 120 (b) 22 (c) 61 (d) 60
21. 21.What is the smallest number of sweets that can be shared equally among 12 children or among 18 children, with none left over? (a) 216 (b) 36 (c) 30 (d) 72
22. 22.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) 20 (b) 2 (c) 12 (d) 4
23. 23.Two bells ring every 6 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 126 min (b) 27 min (c) 3 min (d) 42 min
24. 24.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
25. 25.Two ribbons are 9 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) 3 cm (c) 9 cm (d) 6 cm
26. 26.A teacher has 50 pencils and 70 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 50 (b) 20 (c) 10 (d) 5
27. 27.A teacher has 18 pencils and 42 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 3 (c) 18 (d) 24
28. 28.Two ribbons are 6 cm and 8 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) 24 cm (c) 2 cm (d) 6 cm
29. 29.A teacher has 35 pencils and 42 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) 210 (d) 35
30. 30.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) 5 min (c) 105 min (d) 50 min
31. 31.What is the smallest number of sweets that can be shared equally among 18 children or among 30 children, with none left over? (a) 90 (b) 48 (c) 540 (d) 180
32. 32.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) 108 (d) 36
33. 33.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
34. 34.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) 6 min (b) 120 min (c) 720 min (d) 54 min
35. 35.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) 84 (c) 252 (d) 168
36. 36.What is the smallest number of sweets that can be shared equally among 24 children or among 30 children, with none left over? (a) 54 (b) 720 (c) 240 (d) 120
37. 37.Two bells ring every 20 minutes and every 28 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 560 min (b) 48 min (c) 140 min (d) 4 min
38. 38.A teacher has 27 pencils and 72 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 9 (b) 3 (c) 27 (d) 45
39. 39.A teacher has 8 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) 8 (d) 6
40. 40.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) 140 min (b) 70 min (c) 24 min (d) 2 min

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