HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 412 · 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 96 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) 96 (c) 864 (d) 12
2. 2.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) 3 min (b) 189 min (c) 63 min (d) 30 min
3. 3.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) 150 (c) 300 (d) 55
4. 4.Two ribbons are 60 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) 12 cm (b) 360 cm (c) 60 cm (d) 6 cm
5. 5.Two ribbons are 6 cm and 10 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) 2 cm (d) 4 cm
6. 6.A teacher has 12 pencils and 16 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 48 (b) 12 (c) 2 (d) 4
7. 7.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) 220 cm (b) 11 cm (c) 1 cm (d) 44 cm
8. 8.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) 48 min (d) 2 min
9. 9.A teacher has 10 pencils and 14 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 4 (b) 1 (c) 10 (d) 2
10. 10.A teacher has 45 pencils and 63 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 18 (b) 45 (c) 9 (d) 3
11. 11.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) 12 (b) 48 (c) 6 (d) 240
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) 30 min (b) 216 min (c) 36 min (d) 6 min
13. 13.Two bells ring every 8 minutes and every 12 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 96 min (b) 20 min (c) 24 min (d) 4 min
14. 14.What is the smallest number of sweets that can be shared equally among 4 children or among 6 children, with none left over? (a) 24 (b) 12 (c) 10 (d) 13
15. 15.Two ribbons are 18 cm and 81 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) 63 cm (d) 18 cm
16. 16.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) 54 min (b) 504 min (c) 84 min (d) 6 min
17. 17.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) 90 min (b) 30 min (c) 21 min (d) 3 min
18. 18.Two ribbons are 25 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) 25 cm (b) 20 cm (c) 5 cm (d) 1 cm
19. 19.A teacher has 14 pencils and 35 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 14 (b) 21 (c) 7 (d) 1
20. 20.What is the smallest number of sweets that can be shared equally among 6 children or among 15 children, with none left over? (a) 30 (b) 21 (c) 60 (d) 90
21. 21.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) 24 min (b) 70 min (c) 140 min (d) 2 min
22. 22.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) 24 (c) 3 (d) 6
23. 23.What is the smallest number of sweets that can be shared equally among 15 children or among 20 children, with none left over? (a) 35 (b) 60 (c) 120 (d) 300
24. 24.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) 120 (c) 240 (d) 54
25. 25.Two bells ring every 25 minutes and every 30 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 5 min (b) 55 min (c) 150 min (d) 750 min
26. 26.Two bells ring every 18 minutes and every 24 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 432 min (b) 6 min (c) 42 min (d) 72 min
27. 27.What is the smallest number of sweets that can be shared equally among 4 children or among 14 children, with none left over? (a) 56 (b) 29 (c) 18 (d) 28
28. 28.What is the smallest number of sweets that can be shared equally among 12 children or among 20 children, with none left over? (a) 60 (b) 32 (c) 120 (d) 240
29. 29.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) 9 (b) 1 (c) 15 (d) 3
30. 30.A teacher has 60 pencils and 72 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 60 (b) 360 (c) 6 (d) 12
31. 31.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) 20 (c) 4 (d) 2
32. 32.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) 21 cm (c) 7 cm (d) 14 cm
33. 33.A teacher has 20 pencils and 45 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 20 (b) 25 (c) 1 (d) 5
34. 34.A teacher has 12 pencils and 32 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 20 (b) 12 (c) 4 (d) 2
35. 35.What is the smallest number of sweets that can be shared equally among 12 children or among 28 children, with none left over? (a) 168 (b) 84 (c) 40 (d) 336
36. 36.Two ribbons are 14 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) 42 cm (c) 14 cm (d) 7 cm
37. 37.A teacher has 24 pencils and 28 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 4 (b) 2 (c) 168 (d) 24
38. 38.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) 6 (b) 18 (c) 3 (d) 1
39. 39.Two ribbons are 35 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) 210 cm (b) 7 cm (c) 35 cm (d) 1 cm
40. 40.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) 330 (b) 11 (c) 55 (d) 1

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