HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 310 · 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 9 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) 3 (c) 9 (d) 6
2. 2.Two ribbons are 28 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) 28 cm (b) 224 cm (c) 2 cm (d) 4 cm
3. 3.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) 36 (d) 21
4. 4.Two ribbons are 28 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) 1 cm (b) 21 cm (c) 7 cm (d) 28 cm
5. 5.A teacher has 77 pencils and 99 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 77 (c) 11 (d) 22
6. 6.Two ribbons are 20 cm and 90 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 70 cm (b) 10 cm (c) 20 cm (d) 5 cm
7. 7.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) 6 min (c) 30 min (d) 36 min
8. 8.What is the smallest number of sweets that can be shared equally among 6 children or among 8 children, with none left over? (a) 24 (b) 48 (c) 25 (d) 14
9. 9.A teacher has 28 pencils and 63 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 7 (b) 1 (c) 28 (d) 35
10. 10.A teacher has 16 pencils and 18 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 2 (b) 16 (c) 144 (d) 1
11. 11.A teacher has 55 pencils and 66 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 55 (b) 1 (c) 11 (d) 330
12. 12.Two ribbons are 18 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) 126 cm (b) 1 cm (c) 18 cm (d) 3 cm
13. 13.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) 112 min (b) 448 min (c) 44 min (d) 4 min
14. 14.Two ribbons are 22 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) 1 cm (b) 22 cm (c) 77 cm (d) 11 cm
15. 15.A teacher has 36 pencils and 81 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 45 (b) 3 (c) 36 (d) 9
16. 16.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) 2 min (c) 18 min (d) 28 min
17. 17.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
18. 18.What is the smallest number of sweets that can be shared equally among 9 children or among 15 children, with none left over? (a) 90 (b) 24 (c) 135 (d) 45
19. 19.Two ribbons are 25 cm and 30 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) 5 cm (c) 25 cm (d) 150 cm
20. 20.A teacher has 44 pencils and 55 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 220 (b) 44 (c) 11 (d) 1
21. 21.What is the smallest number of sweets that can be shared equally among 18 children or among 42 children, with none left over? (a) 60 (b) 756 (c) 126 (d) 252
22. 22.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) 3 min (c) 108 min (d) 36 min
23. 23.Two ribbons are 10 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) 10 cm (b) 15 cm (c) 5 cm (d) 1 cm
24. 24.What is the smallest number of sweets that can be shared equally among 10 children or among 14 children, with none left over? (a) 24 (b) 140 (c) 70 (d) 71
25. 25.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) 1 (b) 35 (c) 7 (d) 21
26. 26.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) 250 min (c) 35 min (d) 50 min
27. 27.Two ribbons are 6 cm and 27 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) 1 cm (c) 3 cm (d) 21 cm
28. 28.A teacher has 18 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) 3 (c) 24 (d) 6
29. 29.A teacher has 8 pencils and 28 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 20 (b) 8 (c) 2 (d) 4
30. 30.Two ribbons are 40 cm and 50 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) 40 cm (c) 200 cm (d) 10 cm
31. 31.What is the smallest number of sweets that can be shared equally among 10 children or among 35 children, with none left over? (a) 45 (b) 70 (c) 350 (d) 140
32. 32.What is the smallest number of sweets that can be shared equally among 20 children or among 35 children, with none left over? (a) 55 (b) 280 (c) 140 (d) 700
33. 33.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) 3 min (c) 126 min (d) 27 min
34. 34.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) 10 cm (c) 1 cm (d) 5 cm
35. 35.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) 2 cm (b) 8 cm (c) 4 cm (d) 12 cm
36. 36.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) 70 min (b) 140 min (c) 24 min (d) 2 min
37. 37.A teacher has 36 pencils and 96 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 12 (b) 60 (c) 36 (d) 6
38. 38.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) 39 min (b) 126 min (c) 378 min (d) 3 min
39. 39.Two ribbons are 18 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) 18 cm (c) 24 cm (d) 3 cm
40. 40.Two bells ring every 12 minutes and every 15 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 180 min (b) 60 min (c) 27 min (d) 3 min

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