HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 839 · 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 56 pencils and 64 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 4 (b) 448 (c) 56 (d) 8
2. 2.Two ribbons are 21 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) 28 cm (b) 7 cm (c) 21 cm (d) 1 cm
3. 3.A teacher has 60 pencils and 108 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 60 (c) 48 (d) 12
4. 4.A teacher has 6 pencils and 9 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 18 (c) 3 (d) 6
5. 5.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) 14 (c) 48 (d) 24
6. 6.What is the smallest number of sweets that can be shared equally among 20 children or among 24 children, with none left over? (a) 120 (b) 44 (c) 240 (d) 480
7. 7.What is the smallest number of sweets that can be shared equally among 12 children or among 18 children, with none left over? (a) 72 (b) 30 (c) 216 (d) 36
8. 8.A teacher has 30 pencils and 80 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 30 (b) 10 (c) 50 (d) 5
9. 9.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) 20 (b) 5 (c) 1 (d) 15
10. 10.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) 504 min (b) 54 min (c) 6 min (d) 84 min
11. 11.Two ribbons are 8 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) 2 cm (b) 28 cm (c) 4 cm (d) 8 cm
12. 12.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) 720 min (b) 120 min (c) 6 min (d) 54 min
13. 13.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) 240 (b) 8 (c) 4 (d) 40
14. 14.A teacher has 84 pencils and 96 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 672 (c) 12 (d) 84
15. 15.Two bells ring every 8 minutes and every 20 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 160 min (b) 28 min (c) 40 min (d) 4 min
16. 16.What is the smallest number of sweets that can be shared equally among 10 children or among 15 children, with none left over? (a) 25 (b) 30 (c) 60 (d) 150
17. 17.Two ribbons are 42 cm and 48 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 42 cm (b) 3 cm (c) 6 cm (d) 336 cm
18. 18.Two ribbons are 18 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) 3 cm (b) 27 cm (c) 18 cm (d) 9 cm
19. 19.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
20. 20.What is the smallest number of sweets that can be shared equally among 8 children or among 20 children, with none left over? (a) 28 (b) 160 (c) 80 (d) 40
21. 21.What is the smallest number of sweets that can be shared equally among 6 children or among 9 children, with none left over? (a) 54 (b) 15 (c) 18 (d) 36
22. 22.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) 12 min (b) 24 min (c) 10 min (d) 2 min
23. 23.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) 44 min (c) 4 min (d) 448 min
24. 24.Two ribbons are 21 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) 3 cm (c) 1 cm (d) 21 cm
25. 25.A teacher has 27 pencils and 63 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 36 (c) 9 (d) 27
26. 26.Two ribbons are 55 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) 55 cm (b) 22 cm (c) 11 cm (d) 1 cm
27. 27.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) 36 min (b) 108 min (c) 3 min (d) 21 min
28. 28.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) 2 min (b) 22 min (c) 56 min (d) 112 min
29. 29.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) 22 min (b) 120 min (c) 2 min (d) 60 min
30. 30.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) 6 cm (b) 1 cm (c) 10 cm (d) 2 cm
31. 31.What is the smallest number of sweets that can be shared equally among 12 children or among 15 children, with none left over? (a) 60 (b) 180 (c) 120 (d) 27
32. 32.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) 126 (d) 84
33. 33.What is the smallest number of sweets that can be shared equally among 15 children or among 25 children, with none left over? (a) 40 (b) 75 (c) 150 (d) 375
34. 34.What is the smallest number of sweets that can be shared equally among 10 children or among 25 children, with none left over? (a) 50 (b) 35 (c) 250 (d) 100
35. 35.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) 25 cm (b) 1 cm (c) 5 cm (d) 150 cm
36. 36.A teacher has 16 pencils and 56 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 4 (b) 16 (c) 8 (d) 40
37. 37.Two bells ring every 6 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 42 min (b) 2 min (c) 20 min (d) 84 min
38. 38.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) 4 min (b) 120 min (c) 44 min (d) 480 min
39. 39.Two ribbons are 27 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) 27 cm (b) 18 cm (c) 3 cm (d) 9 cm
40. 40.What is the smallest number of sweets that can be shared equally among 15 children or among 21 children, with none left over? (a) 105 (b) 315 (c) 210 (d) 36

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