HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 632 · 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 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) 8 (b) 2 (c) 4 (d) 20
2. 2.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) 4 cm (c) 28 cm (d) 8 cm
3. 3.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) 24 min (b) 14 min (c) 2 min (d) 48 min
4. 4.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) 150 min (b) 30 min (c) 5 min (d) 25 min
5. 5.Two ribbons are 72 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) 6 cm (b) 12 cm (c) 504 cm (d) 72 cm
6. 6.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) 336 min (b) 84 min (c) 40 min (d) 4 min
7. 7.A teacher has 30 pencils and 50 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 30 (b) 20 (c) 5 (d) 10
8. 8.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) 12 cm (c) 30 cm (d) 3 cm
9. 9.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) 45 min (b) 70 min (c) 5 min (d) 350 min
10. 10.Two bells ring every 4 minutes and every 10 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 14 min (b) 40 min (c) 2 min (d) 20 min
11. 11.A teacher has 8 pencils and 12 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 8 (b) 4 (c) 24 (d) 2
12. 12.Two ribbons are 40 cm and 64 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) 24 cm (c) 8 cm (d) 40 cm
13. 13.A teacher has 22 pencils and 99 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 22 (b) 11 (c) 1 (d) 77
14. 14.What is the smallest number of sweets that can be shared equally among 18 children or among 42 children, with none left over? (a) 252 (b) 756 (c) 60 (d) 126
15. 15.Two ribbons are 56 cm and 63 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) 504 cm (c) 56 cm (d) 1 cm
16. 16.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
17. 17.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) 1 cm (b) 88 cm (c) 792 cm (d) 11 cm
18. 18.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) 21 min (d) 36 min
19. 19.Two bells ring every 12 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 84 min (b) 168 min (c) 2 min (d) 26 min
20. 20.A teacher has 36 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
21. 21.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) 11 (b) 44 (c) 220 (d) 1
22. 22.A teacher has 40 pencils and 45 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 360 (b) 5 (c) 40 (d) 1
23. 23.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) 9 cm (b) 3 cm (c) 45 cm (d) 270 cm
24. 24.A teacher has 16 pencils and 24 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 48 (b) 8 (c) 4 (d) 16
25. 25.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) 20 min (b) 2 min (c) 84 min (d) 42 min
26. 26.What is the smallest number of sweets that can be shared equally among 18 children or among 30 children, with none left over? (a) 90 (b) 48 (c) 540 (d) 180
27. 27.What is the smallest number of sweets that can be shared equally among 8 children or among 12 children, with none left over? (a) 20 (b) 24 (c) 48 (d) 96
28. 28.A teacher has 9 pencils and 24 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) 3 (d) 9
29. 29.What is the smallest number of sweets that can be shared equally among 12 children or among 18 children, with none left over? (a) 216 (b) 30 (c) 36 (d) 72
30. 30.A teacher has 8 pencils and 20 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 2 (b) 4 (c) 12 (d) 8
31. 31.Two bells ring every 15 minutes and every 20 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 60 min (b) 300 min (c) 35 min (d) 5 min
32. 32.What is the smallest number of sweets that can be shared equally among 8 children or among 14 children, with none left over? (a) 112 (b) 57 (c) 56 (d) 22
33. 33.What is the smallest number of sweets that can be shared equally among 10 children or among 25 children, with none left over? (a) 100 (b) 35 (c) 50 (d) 250
34. 34.What is the smallest number of sweets that can be shared equally among 24 children or among 30 children, with none left over? (a) 720 (b) 240 (c) 54 (d) 120
35. 35.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) 27 (d) 60
36. 36.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) 7 (b) 14 (c) 35 (d) 1
37. 37.Two ribbons are 77 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) 616 cm (b) 77 cm (c) 1 cm (d) 11 cm
38. 38.Two ribbons are 20 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) 20 cm (b) 16 cm (c) 4 cm (d) 2 cm
39. 39.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) 33 cm (b) 11 cm (c) 1 cm (d) 44 cm
40. 40.A teacher has 6 pencils and 27 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 21 (b) 3 (c) 6 (d) 1

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