HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 961 · 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 50 pencils and 70 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 50 (b) 5 (c) 10 (d) 20
2. 2.Two bells ring every 15 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 36 min (b) 315 min (c) 105 min (d) 3 min
3. 3.What is the smallest number of sweets that can be shared equally among 20 children or among 24 children, with none left over? (a) 240 (b) 480 (c) 120 (d) 44
4. 4.Two ribbons are 9 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) 12 cm (b) 3 cm (c) 9 cm (d) 1 cm
5. 5.Two ribbons are 12 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) 2 cm (b) 84 cm (c) 1 cm (d) 12 cm
6. 6.A teacher has 18 pencils and 30 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 18 (b) 6 (c) 12 (d) 3
7. 7.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) 70 min (b) 140 min (c) 24 min (d) 2 min
8. 8.Two ribbons are 10 cm and 15 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) 1 cm (c) 5 cm (d) 10 cm
9. 9.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) 48 min (b) 14 min (c) 2 min (d) 24 min
10. 10.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) 85 (c) 84 (d) 168
11. 11.A teacher has 6 pencils and 14 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 8 (c) 2 (d) 6
12. 12.Two ribbons are 48 cm and 60 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 48 cm (b) 6 cm (c) 240 cm (d) 12 cm
13. 13.A teacher has 24 pencils and 36 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 72 (c) 12 (d) 24
14. 14.Two ribbons are 88 cm and 99 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) 88 cm (c) 792 cm (d) 11 cm
15. 15.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) 60 (c) 27 (d) 120
16. 16.A teacher has 50 pencils and 60 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 50 (b) 10 (c) 300 (d) 5
17. 17.A teacher has 22 pencils and 99 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 77 (b) 22 (c) 11 (d) 1
18. 18.Two ribbons are 40 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) 40 cm (c) 8 cm (d) 4 cm
19. 19.Two bells ring every 12 minutes and every 28 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 84 min (b) 336 min (c) 4 min (d) 40 min
20. 20.What is the smallest number of sweets that can be shared equally among 15 children or among 18 children, with none left over? (a) 180 (b) 90 (c) 270 (d) 33
21. 21.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) 28 min (c) 192 min (d) 48 min
22. 22.Two ribbons are 24 cm and 64 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) 4 cm (c) 8 cm (d) 40 cm
23. 23.A teacher has 30 pencils and 40 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 30 (b) 5 (c) 120 (d) 10
24. 24.What is the smallest number of sweets that can be shared equally among 12 children or among 42 children, with none left over? (a) 54 (b) 168 (c) 504 (d) 84
25. 25.A teacher has 22 pencils and 55 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 22 (c) 11 (d) 33
26. 26.A teacher has 55 pencils and 99 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 44 (c) 11 (d) 55
27. 27.What is the smallest number of sweets that can be shared equally among 20 children or among 35 children, with none left over? (a) 55 (b) 140 (c) 700 (d) 280
28. 28.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) 18 min (b) 2 min (c) 28 min (d) 56 min
29. 29.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) 55 (c) 300 (d) 150
30. 30.A teacher has 10 pencils and 25 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 5 (c) 15 (d) 10
31. 31.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) 120 (c) 60 (d) 300
32. 32.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) 11 cm (b) 22 cm (c) 55 cm (d) 1 cm
33. 33.Two ribbons are 4 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) 1 cm (b) 4 cm (c) 2 cm (d) 6 cm
34. 34.A teacher has 40 pencils and 90 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 40 (b) 10 (c) 50 (d) 5
35. 35.What is the smallest number of sweets that can be shared equally among 6 children or among 10 children, with none left over? (a) 60 (b) 16 (c) 31 (d) 30
36. 36.Two ribbons are 20 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) 5 cm (c) 1 cm (d) 20 cm
37. 37.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) 12 cm (b) 6 cm (c) 72 cm (d) 504 cm
38. 38.A teacher has 28 pencils and 35 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 28 (b) 1 (c) 140 (d) 7
39. 39.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) 44 min (b) 4 min (c) 480 min (d) 120 min
40. 40.What is the smallest number of sweets that can be shared equally among 12 children or among 18 children, with none left over? (a) 72 (b) 216 (c) 30 (d) 36

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