HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 720 · 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 ribbons are 21 cm and 24 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 21 cm (b) 1 cm (c) 168 cm (d) 3 cm
2. 2.A teacher has 33 pencils and 88 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 55 (b) 33 (c) 11 (d) 1
3. 3.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) 24 min (b) 140 min (c) 2 min (d) 70 min
4. 4.What is the smallest number of sweets that can be shared equally among 15 children or among 35 children, with none left over? (a) 210 (b) 525 (c) 50 (d) 105
5. 5.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) 11 cm (b) 1 cm (c) 33 cm (d) 22 cm
6. 6.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) 30 min (b) 189 min (c) 3 min (d) 63 min
7. 7.Two ribbons are 12 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) 36 cm (b) 12 cm (c) 3 cm (d) 6 cm
8. 8.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) 216 min (b) 36 min (c) 6 min (d) 30 min
9. 9.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) 2 min (c) 112 min (d) 56 min
10. 10.What is the smallest number of sweets that can be shared equally among 8 children or among 10 children, with none left over? (a) 41 (b) 40 (c) 80 (d) 18
11. 11.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) 120 min (b) 480 min (c) 4 min (d) 44 min
12. 12.What is the smallest number of sweets that can be shared equally among 6 children or among 10 children, with none left over? (a) 16 (b) 60 (c) 30 (d) 31
13. 13.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) 1 (b) 25 (c) 20 (d) 5
14. 14.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) 18 min (b) 56 min (c) 28 min (d) 2 min
15. 15.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) 10 min (c) 2 min (d) 24 min
16. 16.What is the smallest number of sweets that can be shared equally among 4 children or among 10 children, with none left over? (a) 40 (b) 21 (c) 14 (d) 20
17. 17.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) 560 (d) 48
18. 18.A teacher has 6 pencils and 21 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) 15 (d) 3
19. 19.A teacher has 30 pencils and 36 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 30 (c) 3 (d) 180
20. 20.A teacher has 20 pencils and 50 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 5 (b) 30 (c) 20 (d) 10
21. 21.Two ribbons are 28 cm and 32 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) 28 cm (c) 224 cm (d) 4 cm
22. 22.A teacher has 84 pencils and 108 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 84 (b) 12 (c) 24 (d) 6
23. 23.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
24. 24.A teacher has 30 pencils and 35 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 5 (c) 30 (d) 210
25. 25.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) 108 (c) 36 (d) 21
26. 26.A teacher has 88 pencils and 99 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 88 (b) 1 (c) 792 (d) 11
27. 27.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) 18 min (c) 3 min (d) 15 min
28. 28.What is the smallest number of sweets that can be shared equally among 12 children or among 28 children, with none left over? (a) 336 (b) 40 (c) 168 (d) 84
29. 29.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) 40 min (b) 14 min (c) 2 min (d) 20 min
30. 30.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) 720 min (b) 6 min (c) 120 min (d) 54 min
31. 31.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) 22 min (b) 60 min (c) 2 min (d) 120 min
32. 32.A teacher has 77 pencils and 99 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 77 (b) 11 (c) 1 (d) 22
33. 33.Two bells ring every 12 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 26 min (b) 84 min (c) 168 min (d) 2 min
34. 34.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) 15 cm (b) 5 cm (c) 1 cm (d) 25 cm
35. 35.What is the smallest number of sweets that can be shared equally among 4 children or among 6 children, with none left over? (a) 13 (b) 24 (c) 12 (d) 10
36. 36.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) 126 min (b) 6 min (c) 756 min (d) 60 min
37. 37.Two bells ring every 10 minutes and every 35 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 70 min (b) 5 min (c) 350 min (d) 45 min
38. 38.Two ribbons are 14 cm and 21 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 14 cm (b) 7 cm (c) 1 cm (d) 42 cm
39. 39.A teacher has 10 pencils and 12 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 10 (b) 2 (c) 60 (d) 1
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) 90 (b) 180 (c) 33 (d) 270

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