HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 559 · 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.A teacher has 6 pencils and 15 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 9 (c) 6 (d) 3
2. 2.Two bells ring every 8 minutes and every 28 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 36 min (b) 4 min (c) 224 min (d) 56 min
3. 3.Two ribbons are 35 cm and 45 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 35 cm (b) 5 cm (c) 10 cm (d) 1 cm
4. 4.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) 140 min (b) 55 min (c) 5 min (d) 700 min
5. 5.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) 16 min (b) 2 min (c) 30 min (d) 60 min
6. 6.Two ribbons are 10 cm and 45 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) 10 cm (c) 1 cm (d) 35 cm
7. 7.What is the smallest number of sweets that can be shared equally among 9 children or among 15 children, with none left over? (a) 135 (b) 24 (c) 45 (d) 90
8. 8.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) 140 min (c) 4 min (d) 48 min
9. 9.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) 3 min (c) 30 min (d) 189 min
10. 10.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) 25 (c) 24 (d) 48
11. 11.Two ribbons are 56 cm and 72 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 4 cm (b) 8 cm (c) 56 cm (d) 16 cm
12. 12.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) 90 min (b) 33 min (c) 270 min (d) 3 min
13. 13.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) 3 min (c) 33 min (d) 252 min
14. 14.A teacher has 12 pencils and 21 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 9 (b) 12 (c) 1 (d) 3
15. 15.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) 108 min (b) 3 min (c) 36 min (d) 21 min
16. 16.A teacher has 56 pencils and 63 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 56 (b) 1 (c) 504 (d) 7
17. 17.A teacher has 35 pencils and 45 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 5 (b) 1 (c) 35 (d) 10
18. 18.Two ribbons are 33 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) 33 cm (d) 11 cm
19. 19.Two ribbons are 15 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) 1 cm (b) 15 cm (c) 6 cm (d) 3 cm
20. 20.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) 27 min (b) 126 min (c) 3 min (d) 42 min
21. 21.What is the smallest number of sweets that can be shared equally among 4 children or among 10 children, with none left over? (a) 14 (b) 21 (c) 40 (d) 20
22. 22.What is the smallest number of sweets that can be shared equally among 18 children or among 30 children, with none left over? (a) 540 (b) 180 (c) 90 (d) 48
23. 23.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) 18 (c) 80 (d) 40
24. 24.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) 3 cm (c) 12 cm (d) 6 cm
25. 25.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) 20 (c) 24 (d) 96
26. 26.What is the smallest number of sweets that can be shared equally among 10 children or among 14 children, with none left over? (a) 140 (b) 24 (c) 71 (d) 70
27. 27.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) 21 (c) 72 (d) 36
28. 28.Two ribbons are 12 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) 60 cm (b) 1 cm (c) 3 cm (d) 12 cm
29. 29.A teacher has 20 pencils and 24 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 20 (b) 4 (c) 120 (d) 2
30. 30.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) 120 (d) 240
31. 31.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) 18 (b) 54 (c) 3 (d) 9
32. 32.A teacher has 70 pencils and 80 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 560 (b) 70 (c) 5 (d) 10
33. 33.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) 6 (b) 240 (c) 12 (d) 48
34. 34.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) 84 min (b) 504 min (c) 54 min (d) 6 min
35. 35.Two ribbons are 42 cm and 49 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) 294 cm (c) 1 cm (d) 42 cm
36. 36.Two ribbons are 55 cm and 88 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 55 cm (b) 33 cm (c) 1 cm (d) 11 cm
37. 37.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) 54 min (c) 120 min (d) 720 min
38. 38.What is the smallest number of sweets that can be shared equally among 20 children or among 24 children, with none left over? (a) 44 (b) 240 (c) 480 (d) 120
39. 39.What is the smallest number of sweets that can be shared equally among 25 children or among 30 children, with none left over? (a) 750 (b) 300 (c) 55 (d) 150
40. 40.Two ribbons are 20 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) 20 cm (b) 2 cm (c) 4 cm (d) 12 cm

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