HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 174 · 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 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
2. 2.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) 24 min (b) 2 min (c) 12 min (d) 10 min
3. 3.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) 7 cm (b) 1 cm (c) 210 cm (d) 35 cm
4. 4.What is the smallest number of sweets that can be shared equally among 10 children or among 25 children, with none left over? (a) 250 (b) 35 (c) 100 (d) 50
5. 5.A teacher has 12 pencils and 42 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 12 (b) 6 (c) 3 (d) 30
6. 6.Two ribbons are 40 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) 40 cm (b) 8 cm (c) 4 cm (d) 240 cm
7. 7.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
8. 8.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) 28 (d) 18
9. 9.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
10. 10.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) 24 min (b) 96 min (c) 20 min (d) 4 min
11. 11.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) 36 min (c) 30 min (d) 216 min
12. 12.Two ribbons are 21 cm and 28 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 84 cm (b) 1 cm (c) 7 cm (d) 21 cm
13. 13.What is the smallest number of sweets that can be shared equally among 10 children or among 15 children, with none left over? (a) 150 (b) 60 (c) 30 (d) 25
14. 14.What is the smallest number of sweets that can be shared equally among 8 children or among 12 children, with none left over? (a) 24 (b) 20 (c) 48 (d) 96
15. 15.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) 84 min (d) 6 min
16. 16.Two ribbons are 27 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) 108 cm (b) 9 cm (c) 3 cm (d) 27 cm
17. 17.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) 15 (b) 1 (c) 20 (d) 5
18. 18.A teacher has 28 pencils and 36 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 8 (b) 28 (c) 2 (d) 4
19. 19.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) 350 min (b) 70 min (c) 5 min (d) 45 min
20. 20.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) 30 min (b) 21 min (c) 90 min (d) 3 min
21. 21.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) 42 min (c) 6 min (d) 72 min
22. 22.A teacher has 60 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) 60 (c) 12 (d) 36
23. 23.What is the smallest number of sweets that can be shared equally among 15 children or among 25 children, with none left over? (a) 150 (b) 375 (c) 75 (d) 40
24. 24.Two bells ring every 12 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 33 min (b) 84 min (c) 3 min (d) 252 min
25. 25.Two bells ring every 20 minutes and every 35 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 700 min (b) 55 min (c) 140 min (d) 5 min
26. 26.What is the smallest number of sweets that can be shared equally among 12 children or among 15 children, with none left over? (a) 27 (b) 60 (c) 180 (d) 120
27. 27.Two ribbons are 15 cm and 18 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) 1 cm (c) 90 cm (d) 3 cm
28. 28.Two ribbons are 21 cm and 24 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) 168 cm (c) 21 cm (d) 3 cm
29. 29.Two ribbons are 84 cm and 96 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) 672 cm (c) 12 cm (d) 84 cm
30. 30.Two bells ring every 12 minutes and every 16 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 192 min (b) 28 min (c) 48 min (d) 4 min
31. 31.Two ribbons are 15 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) 1 cm (b) 60 cm (c) 15 cm (d) 5 cm
32. 32.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) 35 min (b) 250 min (c) 5 min (d) 50 min
33. 33.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) 45 (c) 24 (d) 135
34. 34.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) 75 min (b) 40 min (c) 5 min (d) 375 min
35. 35.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) 36 (d) 18
36. 36.Two ribbons are 15 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) 5 cm (b) 25 cm (c) 15 cm (d) 1 cm
37. 37.A teacher has 36 pencils and 45 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 9 (b) 36 (c) 3 (d) 180
38. 38.A teacher has 35 pencils and 49 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 14 (b) 7 (c) 35 (d) 1
39. 39.A teacher has 20 pencils and 32 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 2 (b) 20 (c) 4 (d) 12
40. 40.Two ribbons are 35 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) 35 cm (b) 5 cm (c) 1 cm (d) 280 cm

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