HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 606 · 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.What is the smallest number of sweets that can be shared equally among 12 children or among 16 children, with none left over? (a) 96 (b) 48 (c) 28 (d) 192
2. 2.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) 42 min (b) 432 min (c) 6 min (d) 72 min
3. 3.What is the smallest number of sweets that can be shared equally among 4 children or among 14 children, with none left over? (a) 28 (b) 18 (c) 29 (d) 56
4. 4.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) 50 (b) 30 (c) 10 (d) 5
5. 5.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) 12 (b) 672 (c) 84 (d) 6
6. 6.What is the smallest number of sweets that can be shared equally among 6 children or among 9 children, with none left over? (a) 36 (b) 54 (c) 18 (d) 15
7. 7.What is the smallest number of sweets that can be shared equally among 18 children or among 30 children, with none left over? (a) 180 (b) 48 (c) 90 (d) 540
8. 8.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
9. 9.A teacher has 6 pencils and 8 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 2 (c) 24 (d) 6
10. 10.Two bells ring every 8 minutes and every 28 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 4 min (b) 56 min (c) 224 min (d) 36 min
11. 11.What is the smallest number of sweets that can be shared equally among 4 children or among 6 children, with none left over? (a) 12 (b) 10 (c) 13 (d) 24
12. 12.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) 60 (c) 150 (d) 30
13. 13.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) 189 min (b) 63 min (c) 30 min (d) 3 min
14. 14.What is the smallest number of sweets that can be shared equally among 6 children or among 15 children, with none left over? (a) 60 (b) 21 (c) 30 (d) 90
15. 15.Two ribbons are 12 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) 1 cm (b) 15 cm (c) 3 cm (d) 12 cm
16. 16.What is the smallest number of sweets that can be shared equally among 10 children or among 35 children, with none left over? (a) 140 (b) 350 (c) 45 (d) 70
17. 17.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) 1 (d) 3
18. 18.Two ribbons are 25 cm and 40 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 15 cm (b) 25 cm (c) 5 cm (d) 1 cm
19. 19.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) 6 min (c) 120 min (d) 54 min
20. 20.Two ribbons are 27 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) 36 cm (b) 9 cm (c) 3 cm (d) 27 cm
21. 21.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) 60 cm (b) 48 cm (c) 12 cm (d) 6 cm
22. 22.What is the smallest number of sweets that can be shared equally among 10 children or among 12 children, with none left over? (a) 61 (b) 22 (c) 120 (d) 60
23. 23.What is the smallest number of sweets that can be shared equally among 8 children or among 10 children, with none left over? (a) 80 (b) 41 (c) 18 (d) 40
24. 24.Two ribbons are 24 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) 30 cm (b) 24 cm (c) 3 cm (d) 6 cm
25. 25.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) 6 min (b) 30 min (c) 36 min (d) 216 min
26. 26.Two ribbons are 18 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) 18 cm (b) 12 cm (c) 3 cm (d) 6 cm
27. 27.A teacher has 15 pencils and 18 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) 90 (d) 15
28. 28.A teacher has 9 pencils and 12 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 1 (c) 9 (d) 36
29. 29.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) 168 (b) 4 (c) 2 (d) 24
30. 30.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) 3 cm (b) 336 cm (c) 6 cm (d) 42 cm
31. 31.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) 16 (b) 48 (c) 4 (d) 8
32. 32.Two ribbons are 32 cm and 56 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 32 cm (b) 4 cm (c) 8 cm (d) 24 cm
33. 33.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) 5 min (b) 375 min (c) 75 min (d) 40 min
34. 34.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) 150 min (c) 25 min (d) 5 min
35. 35.A teacher has 35 pencils and 42 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 35 (b) 1 (c) 210 (d) 7
36. 36.Two ribbons are 30 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) 3 cm (b) 6 cm (c) 18 cm (d) 30 cm
37. 37.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) 100 (d) 250
38. 38.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) 100 min (b) 5 min (c) 45 min (d) 500 min
39. 39.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) 6 min (b) 84 min (c) 54 min (d) 504 min
40. 40.Two ribbons are 32 cm and 40 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) 160 cm (c) 32 cm (d) 8 cm

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