HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 179 · 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 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) 448 min (c) 112 min (d) 4 min
2. 2.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) 60 min (b) 16 min (c) 2 min (d) 30 min
3. 3.What is the smallest number of sweets that can be shared equally among 6 children or among 21 children, with none left over? (a) 126 (b) 27 (c) 42 (d) 84
4. 4.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) 6 min (b) 36 min (c) 30 min (d) 216 min
5. 5.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) 4 min (c) 480 min (d) 44 min
6. 6.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) 2 min (b) 24 min (c) 12 min (d) 10 min
7. 7.Two bells ring every 12 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 84 min (b) 33 min (c) 252 min (d) 3 min
8. 8.A teacher has 20 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) 15 (c) 20 (d) 5
9. 9.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) 4 min (c) 48 min (d) 140 min
10. 10.What is the smallest number of sweets that can be shared equally among 6 children or among 9 children, with none left over? (a) 36 (b) 54 (c) 18 (d) 15
11. 11.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) 105 (c) 525 (d) 50
12. 12.What is the smallest number of sweets that can be shared equally among 12 children or among 20 children, with none left over? (a) 32 (b) 60 (c) 120 (d) 240
13. 13.Two bells ring every 12 minutes and every 28 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 84 min (b) 336 min (c) 40 min (d) 4 min
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) 2 min (c) 28 min (d) 56 min
15. 15.Two bells ring every 18 minutes and every 24 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 6 min (b) 42 min (c) 72 min (d) 432 min
16. 16.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) 9 cm (b) 3 cm (c) 1 cm (d) 6 cm
17. 17.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) 350 min (b) 5 min (c) 45 min (d) 70 min
18. 18.Two ribbons are 27 cm and 36 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 3 cm (b) 108 cm (c) 27 cm (d) 9 cm
19. 19.Two ribbons are 30 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) 6 cm (b) 24 cm (c) 30 cm (d) 3 cm
20. 20.Two ribbons are 6 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) 1 cm (b) 2 cm (c) 10 cm (d) 6 cm
21. 21.Two ribbons are 48 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) 48 cm (b) 12 cm (c) 60 cm (d) 6 cm
22. 22.Two ribbons are 10 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) 30 cm (b) 1 cm (c) 5 cm (d) 10 cm
23. 23.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) 2 (b) 20 (c) 4 (d) 12
24. 24.What is the smallest number of sweets that can be shared equally among 15 children or among 20 children, with none left over? (a) 300 (b) 35 (c) 120 (d) 60
25. 25.A teacher has 14 pencils and 49 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 35 (b) 1 (c) 7 (d) 14
26. 26.Two ribbons are 33 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) 1 cm (b) 22 cm (c) 33 cm (d) 11 cm
27. 27.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) 120 (c) 60 (d) 27
28. 28.A teacher has 40 pencils and 70 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 5 (b) 40 (c) 30 (d) 10
29. 29.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) 2 min (c) 22 min (d) 112 min
30. 30.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) 4 min (b) 36 min (c) 80 min (d) 320 min
31. 31.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) 63 min (b) 30 min (c) 189 min (d) 3 min
32. 32.What is the smallest number of sweets that can be shared equally among 10 children or among 35 children, with none left over? (a) 140 (b) 45 (c) 70 (d) 350
33. 33.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) 20 cm (c) 5 cm (d) 10 cm
34. 34.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) 42 min (b) 27 min (c) 126 min (d) 3 min
35. 35.Two ribbons are 25 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) 25 cm (b) 1 cm (c) 5 cm (d) 10 cm
36. 36.A teacher has 24 pencils and 54 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) 30 (d) 3
37. 37.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) 36 (b) 12 (c) 144 (d) 6
38. 38.A teacher has 18 pencils and 63 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 18 (b) 9 (c) 3 (d) 45
39. 39.A teacher has 35 pencils and 56 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 21 (b) 1 (c) 7 (d) 35
40. 40.Two ribbons are 12 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) 2 cm (b) 16 cm (c) 4 cm (d) 12 cm

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