HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 391 · 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 20 minutes and every 35 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 5 min (b) 700 min (c) 55 min (d) 140 min
2. 2.What is the smallest number of sweets that can be shared equally among 10 children or among 15 children, with none left over? (a) 60 (b) 150 (c) 30 (d) 25
3. 3.What is the smallest number of sweets that can be shared equally among 4 children or among 6 children, with none left over? (a) 12 (b) 13 (c) 24 (d) 10
4. 4.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) 30 min (c) 5 min (d) 150 min
5. 5.Two bells ring every 12 minutes and every 16 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 28 min (b) 48 min (c) 4 min (d) 192 min
6. 6.A teacher has 40 pencils and 48 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 8 (b) 4 (c) 240 (d) 40
7. 7.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) 54 min (b) 504 min (c) 84 min (d) 6 min
8. 8.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) 378 min (b) 126 min (c) 3 min (d) 39 min
9. 9.What is the smallest number of sweets that can be shared equally among 6 children or among 8 children, with none left over? (a) 25 (b) 24 (c) 14 (d) 48
10. 10.A teacher has 40 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) 50 (c) 40 (d) 5
11. 11.A teacher has 10 pencils and 15 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 10 (b) 1 (c) 30 (d) 5
12. 12.What is the smallest number of sweets that can be shared equally among 20 children or among 28 children, with none left over? (a) 140 (b) 280 (c) 560 (d) 48
13. 13.What is the smallest number of sweets that can be shared equally among 20 children or among 25 children, with none left over? (a) 500 (b) 45 (c) 200 (d) 100
14. 14.Two ribbons are 8 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) 8 cm (b) 4 cm (c) 12 cm (d) 2 cm
15. 15.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) 50 min (c) 35 min (d) 250 min
16. 16.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) 4 (b) 20 (c) 2 (d) 8
17. 17.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) 105 min (c) 3 min (d) 315 min
18. 18.Two ribbons are 55 cm and 66 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) 330 cm (c) 11 cm (d) 55 cm
19. 19.What is the smallest number of sweets that can be shared equally among 12 children or among 14 children, with none left over? (a) 26 (b) 168 (c) 84 (d) 85
20. 20.A teacher has 33 pencils and 55 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 33 (c) 22 (d) 11
21. 21.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) 11 cm (b) 66 cm (c) 22 cm (d) 1 cm
22. 22.What is the smallest number of sweets that can be shared equally among 15 children or among 25 children, with none left over? (a) 375 (b) 40 (c) 150 (d) 75
23. 23.Two bells ring every 6 minutes and every 15 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 3 min (b) 90 min (c) 30 min (d) 21 min
24. 24.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) 120 min (b) 60 min (c) 2 min (d) 22 min
25. 25.What is the smallest number of sweets that can be shared equally among 6 children or among 14 children, with none left over? (a) 84 (b) 43 (c) 42 (d) 20
26. 26.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) 48 (c) 96 (d) 24
27. 27.A teacher has 35 pencils and 40 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 280 (b) 1 (c) 5 (d) 35
28. 28.A teacher has 15 pencils and 18 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 90 (b) 3 (c) 15 (d) 1
29. 29.Two ribbons are 77 cm and 99 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 77 cm (b) 11 cm (c) 1 cm (d) 22 cm
30. 30.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) 168 min (b) 2 min (c) 84 min (d) 26 min
31. 31.A teacher has 40 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) 40 (c) 360 (d) 5
32. 32.Two ribbons are 72 cm and 84 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 72 cm (b) 6 cm (c) 504 cm (d) 12 cm
33. 33.A teacher has 18 pencils and 27 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 54 (b) 18 (c) 3 (d) 9
34. 34.Two ribbons are 28 cm and 35 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) 28 cm (c) 140 cm (d) 1 cm
35. 35.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
36. 36.Two bells ring every 15 minutes and every 25 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 40 min (b) 375 min (c) 75 min (d) 5 min
37. 37.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) 44 min (b) 4 min (c) 448 min (d) 112 min
38. 38.What is the smallest number of sweets that can be shared equally among 20 children or among 35 children, with none left over? (a) 700 (b) 280 (c) 140 (d) 55
39. 39.Two ribbons are 22 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) 55 cm (c) 11 cm (d) 1 cm
40. 40.A teacher has 48 pencils and 60 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 240 (b) 48 (c) 6 (d) 12

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