HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 386 · 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 15 pencils and 25 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 15 (b) 10 (c) 1 (d) 5
2. 2.Two bells ring every 12 minutes and every 30 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 6 min (b) 42 min (c) 360 min (d) 60 min
3. 3.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) 480 min (c) 120 min (d) 44 min
4. 4.Two ribbons are 9 cm and 12 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) 1 cm (c) 36 cm (d) 9 cm
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 ribbons are 32 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) 32 cm (b) 4 cm (c) 40 cm (d) 8 cm
7. 7.What is the smallest number of sweets that can be shared equally among 12 children or among 42 children, with none left over? (a) 504 (b) 54 (c) 168 (d) 84
8. 8.Two bells ring every 15 minutes and every 35 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 5 min (b) 525 min (c) 50 min (d) 105 min
9. 9.Two ribbons are 32 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) 4 cm (b) 32 cm (c) 288 cm (d) 2 cm
10. 10.Two ribbons are 28 cm and 32 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) 224 cm
11. 11.Two ribbons are 22 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) 1 cm (c) 11 cm (d) 22 cm
12. 12.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) 36 min (d) 21 min
13. 13.What is the smallest number of sweets that can be shared equally among 12 children or among 15 children, with none left over? (a) 120 (b) 180 (c) 27 (d) 60
14. 14.A teacher has 18 pencils and 27 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 54 (c) 18 (d) 9
15. 15.Two ribbons are 6 cm and 14 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) 2 cm (c) 8 cm (d) 1 cm
16. 16.Two ribbons are 36 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) 144 cm (b) 6 cm (c) 12 cm (d) 36 cm
17. 17.A teacher has 40 pencils and 70 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 10 (b) 40 (c) 5 (d) 30
18. 18.A teacher has 12 pencils and 28 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 12 (b) 4 (c) 16 (d) 2
19. 19.A teacher has 27 pencils and 72 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 45 (c) 9 (d) 27
20. 20.What is the smallest number of sweets that can be shared equally among 18 children or among 42 children, with none left over? (a) 756 (b) 252 (c) 60 (d) 126
21. 21.What is the smallest number of sweets that can be shared equally among 24 children or among 30 children, with none left over? (a) 120 (b) 54 (c) 240 (d) 720
22. 22.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) 36 (b) 3 (c) 180 (d) 9
23. 23.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) 26 min (b) 84 min (c) 2 min (d) 168 min
24. 24.What is the smallest number of sweets that can be shared equally among 12 children or among 14 children, with none left over? (a) 26 (b) 84 (c) 168 (d) 85
25. 25.Two bells ring every 4 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 28 min (b) 18 min (c) 56 min (d) 2 min
26. 26.What is the smallest number of sweets that can be shared equally among 4 children or among 10 children, with none left over? (a) 14 (b) 40 (c) 21 (d) 20
27. 27.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) 252 min (c) 3 min (d) 84 min
28. 28.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) 5 min (c) 35 min (d) 300 min
29. 29.What is the smallest number of sweets that can be shared equally among 10 children or among 14 children, with none left over? (a) 71 (b) 70 (c) 140 (d) 24
30. 30.Two ribbons are 18 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) 9 cm (b) 45 cm (c) 18 cm (d) 3 cm
31. 31.What is the smallest number of sweets that can be shared equally among 4 children or among 6 children, with none left over? (a) 13 (b) 12 (c) 10 (d) 24
32. 32.Two ribbons are 10 cm and 25 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 10 cm (b) 5 cm (c) 15 cm (d) 1 cm
33. 33.A teacher has 4 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
34. 34.What is the smallest number of sweets that can be shared equally among 9 children or among 15 children, with none left over? (a) 135 (b) 24 (c) 90 (d) 45
35. 35.A teacher has 30 pencils and 42 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 30 (b) 12 (c) 3 (d) 6
36. 36.Two ribbons are 15 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) 3 cm (c) 12 cm (d) 15 cm
37. 37.Two bells ring every 16 minutes and every 20 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 36 min (b) 4 min (c) 80 min (d) 320 min
38. 38.What is the smallest number of sweets that can be shared equally among 4 children or among 14 children, with none left over? (a) 29 (b) 56 (c) 28 (d) 18
39. 39.Two bells ring every 15 minutes and every 18 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 90 min (b) 270 min (c) 33 min (d) 3 min
40. 40.What is the smallest number of sweets that can be shared equally among 18 children or among 21 children, with none left over? (a) 126 (b) 252 (c) 378 (d) 39

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