HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 189 · 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 24 pencils and 36 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 12 (b) 24 (c) 6 (d) 72
2. 2.Two bells ring every 12 minutes and every 30 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 360 min (b) 6 min (c) 42 min (d) 60 min
3. 3.What is the smallest number of sweets that can be shared equally among 15 children or among 18 children, with none left over? (a) 33 (b) 90 (c) 180 (d) 270
4. 4.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) 4 min (b) 112 min (c) 44 min (d) 448 min
5. 5.Two ribbons are 44 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) 44 cm (b) 1 cm (c) 220 cm (d) 11 cm
6. 6.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
7. 7.Two ribbons are 21 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) 1 cm (b) 7 cm (c) 21 cm (d) 14 cm
8. 8.Two ribbons are 10 cm and 14 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 10 cm (b) 4 cm (c) 1 cm (d) 2 cm
9. 9.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) 5 min (b) 500 min (c) 100 min (d) 45 min
10. 10.Two ribbons are 24 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) 12 cm (b) 60 cm (c) 6 cm (d) 24 cm
11. 11.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) 150 (c) 40 (d) 75
12. 12.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) 30 min (c) 6 min (d) 36 min
13. 13.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) 21 min (c) 90 min (d) 30 min
14. 14.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) 12 cm (b) 48 cm (c) 60 cm (d) 6 cm
15. 15.Two ribbons are 15 cm and 25 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) 10 cm (c) 5 cm (d) 15 cm
16. 16.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) 48 (c) 140 (d) 280
17. 17.Two bells ring every 6 minutes and every 8 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 2 min (b) 48 min (c) 14 min (d) 24 min
18. 18.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) 2 min (b) 56 min (c) 28 min (d) 18 min
19. 19.A teacher has 24 pencils and 60 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 24 (b) 6 (c) 36 (d) 12
20. 20.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) 375 min (b) 5 min (c) 40 min (d) 75 min
21. 21.What is the smallest number of sweets that can be shared equally among 6 children or among 21 children, with none left over? (a) 27 (b) 42 (c) 84 (d) 126
22. 22.A teacher has 63 pencils and 81 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 9 (c) 63 (d) 18
23. 23.What is the smallest number of sweets that can be shared equally among 9 children or among 15 children, with none left over? (a) 24 (b) 45 (c) 90 (d) 135
24. 24.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) 2 min (b) 70 min (c) 140 min (d) 24 min
25. 25.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) 10 min (b) 24 min (c) 12 min (d) 2 min
26. 26.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) 756 min (b) 6 min (c) 60 min (d) 126 min
27. 27.Two ribbons are 88 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) 792 cm (b) 1 cm (c) 88 cm (d) 11 cm
28. 28.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) 30 min (b) 5 min (c) 150 min (d) 25 min
29. 29.Two ribbons are 12 cm and 42 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) 30 cm (c) 12 cm (d) 3 cm
30. 30.Two ribbons are 14 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) 1 cm (b) 21 cm (c) 7 cm (d) 14 cm
31. 31.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
32. 32.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
33. 33.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) 140 (c) 55 (d) 280
34. 34.A teacher has 80 pencils and 90 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 720 (b) 5 (c) 80 (d) 10
35. 35.A teacher has 54 pencils and 63 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 9 (b) 378 (c) 3 (d) 54
36. 36.A teacher has 12 pencils and 28 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 16 (b) 2 (c) 12 (d) 4
37. 37.Two ribbons are 6 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) 1 cm (b) 9 cm (c) 6 cm (d) 3 cm
38. 38.Two ribbons are 45 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) 270 cm (b) 3 cm (c) 9 cm (d) 45 cm
39. 39.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) 25 (b) 5 (c) 20 (d) 1
40. 40.Two ribbons are 33 cm and 44 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 33 cm (b) 11 cm (c) 132 cm (d) 1 cm

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