HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 355 · 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 14 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) 14 cm (b) 4 cm (c) 2 cm (d) 1 cm
2. 2.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) 96 (c) 48 (d) 24
3. 3.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) 35 min (b) 60 min (c) 300 min (d) 5 min
4. 4.A teacher has 9 pencils and 21 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 12 (b) 9 (c) 1 (d) 3
5. 5.Two ribbons are 12 cm and 16 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) 48 cm (c) 4 cm (d) 2 cm
6. 6.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
7. 7.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) 56 min (b) 28 min (c) 2 min (d) 18 min
8. 8.A teacher has 35 pencils and 49 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 7 (b) 14 (c) 1 (d) 35
9. 9.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) 4 min (b) 24 min (c) 20 min (d) 96 min
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) 25 (c) 60 (d) 30
11. 11.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) 3 min (b) 42 min (c) 126 min (d) 27 min
12. 12.A teacher has 18 pencils and 21 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 18 (b) 126 (c) 1 (d) 3
13. 13.A teacher has 12 pencils and 18 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 12 (c) 36 (d) 6
14. 14.What is the smallest number of sweets that can be shared equally among 9 children or among 12 children, with none left over? (a) 108 (b) 72 (c) 21 (d) 36
15. 15.What is the smallest number of sweets that can be shared equally among 12 children or among 42 children, with none left over? (a) 168 (b) 84 (c) 54 (d) 504
16. 16.What is the smallest number of sweets that can be shared equally among 10 children or among 12 children, with none left over? (a) 22 (b) 120 (c) 60 (d) 61
17. 17.A teacher has 40 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) 200 (c) 40 (d) 10
18. 18.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
19. 19.Two ribbons are 50 cm and 70 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 50 cm (b) 10 cm (c) 5 cm (d) 20 cm
20. 20.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) 36 min (c) 108 min (d) 3 min
21. 21.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) 56 min (b) 22 min (c) 2 min (d) 112 min
22. 22.A teacher has 36 pencils and 48 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 144 (b) 12 (c) 6 (d) 36
23. 23.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) 180 (c) 540 (d) 48
24. 24.What is the smallest number of sweets that can be shared equally among 6 children or among 8 children, with none left over? (a) 14 (b) 48 (c) 24 (d) 25
25. 25.What is the smallest number of sweets that can be shared equally among 8 children or among 14 children, with none left over? (a) 56 (b) 57 (c) 112 (d) 22
26. 26.What is the smallest number of sweets that can be shared equally among 20 children or among 28 children, with none left over? (a) 560 (b) 280 (c) 48 (d) 140
27. 27.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) 105 min (b) 50 min (c) 5 min (d) 525 min
28. 28.What is the smallest number of sweets that can be shared equally among 4 children or among 14 children, with none left over? (a) 29 (b) 28 (c) 56 (d) 18
29. 29.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) 45 min (d) 5 min
30. 30.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) 3 min (b) 378 min (c) 126 min (d) 39 min
31. 31.Two ribbons are 8 cm and 28 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 8 cm (b) 2 cm (c) 20 cm (d) 4 cm
32. 32.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) 27 (c) 60 (d) 120
33. 33.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) 10 min (c) 2 min (d) 12 min
34. 34.Two ribbons are 60 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) 6 cm (b) 60 cm (c) 12 cm (d) 48 cm
35. 35.Two bells ring every 15 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 36 min (b) 3 min (c) 105 min (d) 315 min
36. 36.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) 18 (b) 6 (c) 3 (d) 24
37. 37.A teacher has 70 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) 20 (c) 70 (d) 5
38. 38.Two ribbons are 21 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) 1 cm (b) 21 cm (c) 35 cm (d) 7 cm
39. 39.A teacher has 20 pencils and 90 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 20 (b) 10 (c) 70 (d) 5
40. 40.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

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