HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 11 · 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 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) 5 (b) 40 (c) 1 (d) 360
2. 2.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) 5 min (b) 50 min (c) 35 min (d) 250 min
3. 3.What is the smallest number of sweets that can be shared equally among 16 children or among 20 children, with none left over? (a) 320 (b) 80 (c) 160 (d) 36
4. 4.A teacher has 42 pencils and 54 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 12 (b) 42 (c) 3 (d) 6
5. 5.Two bells ring every 6 minutes and every 9 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 15 min (b) 54 min (c) 18 min (d) 3 min
6. 6.Two ribbons are 70 cm and 90 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) 70 cm (c) 20 cm (d) 10 cm
7. 7.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
8. 8.Two ribbons are 28 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) 7 cm (b) 1 cm (c) 28 cm (d) 140 cm
9. 9.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) 5 (b) 25 (c) 20 (d) 1
10. 10.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) 21 cm (c) 168 cm (d) 3 cm
11. 11.What is the smallest number of sweets that can be shared equally among 8 children or among 12 children, with none left over? (a) 96 (b) 20 (c) 24 (d) 48
12. 12.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) 24 min (c) 4 min (d) 20 min
13. 13.Two bells ring every 18 minutes and every 30 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 90 min (b) 48 min (c) 540 min (d) 6 min
14. 14.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) 672 cm (b) 84 cm (c) 12 cm (d) 6 cm
15. 15.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) 44 (b) 220 (c) 11 (d) 1
16. 16.Two ribbons are 33 cm and 44 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 11 cm (b) 1 cm (c) 132 cm (d) 33 cm
17. 17.Two ribbons are 20 cm and 90 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) 5 cm (c) 70 cm (d) 10 cm
18. 18.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) 18 cm (b) 9 cm (c) 63 cm (d) 3 cm
19. 19.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) 4 min (b) 192 min (c) 48 min (d) 28 min
20. 20.A teacher has 9 pencils and 21 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 12 (c) 9 (d) 3
21. 21.What is the smallest number of sweets that can be shared equally among 6 children or among 10 children, with none left over? (a) 31 (b) 30 (c) 60 (d) 16
22. 22.What is the smallest number of sweets that can be shared equally among 9 children or among 12 children, with none left over? (a) 21 (b) 36 (c) 108 (d) 72
23. 23.Two ribbons are 36 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) 60 cm (b) 6 cm (c) 12 cm (d) 36 cm
24. 24.A teacher has 22 pencils and 33 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 66 (b) 22 (c) 11 (d) 1
25. 25.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) 105 min (c) 50 min (d) 525 min
26. 26.A teacher has 10 pencils and 35 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 10 (b) 1 (c) 25 (d) 5
27. 27.What is the smallest number of sweets that can be shared equally among 12 children or among 28 children, with none left over? (a) 84 (b) 168 (c) 336 (d) 40
28. 28.Two bells ring every 9 minutes and every 15 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 45 min (b) 3 min (c) 135 min (d) 24 min
29. 29.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) 2 min (b) 84 min (c) 168 min (d) 26 min
30. 30.Two ribbons are 12 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) 2 cm (b) 12 cm (c) 16 cm (d) 4 cm
31. 31.A teacher has 60 pencils and 108 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 60 (b) 6 (c) 48 (d) 12
32. 32.What is the smallest number of sweets that can be shared equally among 12 children or among 21 children, with none left over? (a) 252 (b) 33 (c) 168 (d) 84
33. 33.What is the smallest number of sweets that can be shared equally among 15 children or among 35 children, with none left over? (a) 525 (b) 210 (c) 50 (d) 105
34. 34.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
35. 35.Two ribbons are 60 cm and 70 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 420 cm (b) 60 cm (c) 10 cm (d) 5 cm
36. 36.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) 45 (c) 350 (d) 70
37. 37.Two ribbons are 8 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) 24 cm (b) 2 cm (c) 4 cm (d) 8 cm
38. 38.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) 27 (c) 120 (d) 60
39. 39.A teacher has 10 pencils and 12 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 60 (b) 2 (c) 1 (d) 10
40. 40.Two ribbons are 48 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) 12 cm (b) 6 cm (c) 36 cm (d) 48 cm

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