HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 89 · 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 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) 15 (c) 10 (d) 5
2. 2.What is the smallest number of sweets that can be shared equally among 18 children or among 42 children, with none left over? (a) 252 (b) 756 (c) 126 (d) 60
3. 3.What is the smallest number of sweets that can be shared equally among 6 children or among 10 children, with none left over? (a) 30 (b) 16 (c) 60 (d) 31
4. 4.Two ribbons are 20 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) 20 cm (b) 5 cm (c) 10 cm (d) 60 cm
5. 5.What is the smallest number of sweets that can be shared equally among 8 children or among 12 children, with none left over? (a) 20 (b) 96 (c) 48 (d) 24
6. 6.Two ribbons are 12 cm and 16 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) 48 cm (c) 12 cm (d) 4 cm
7. 7.Two ribbons are 8 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) 8 cm (b) 2 cm (c) 6 cm (d) 1 cm
8. 8.A teacher has 48 pencils and 56 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 48 (b) 336 (c) 4 (d) 8
9. 9.A teacher has 8 pencils and 18 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 8 (b) 2 (c) 10 (d) 1
10. 10.A teacher has 55 pencils and 66 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 55 (b) 11 (c) 330 (d) 1
11. 11.Two ribbons are 6 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) 21 cm (d) 6 cm
12. 12.Two ribbons are 20 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) 16 cm (b) 4 cm (c) 20 cm (d) 2 cm
13. 13.A teacher has 30 pencils and 35 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 5 (b) 1 (c) 30 (d) 210
14. 14.A teacher has 10 pencils and 15 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 5 (b) 30 (c) 10 (d) 1
15. 15.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
16. 16.What is the smallest number of sweets that can be shared equally among 4 children or among 10 children, with none left over? (a) 21 (b) 20 (c) 14 (d) 40
17. 17.Two bells ring every 10 minutes and every 12 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 2 min (b) 22 min (c) 60 min (d) 120 min
18. 18.Two ribbons are 24 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) 24 cm (c) 3 cm (d) 216 cm
19. 19.A teacher has 12 pencils and 16 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 48 (b) 12 (c) 4 (d) 2
20. 20.Two ribbons are 16 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) 48 cm (b) 16 cm (c) 4 cm (d) 8 cm
21. 21.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) 18 (c) 29 (d) 28
22. 22.A teacher has 33 pencils and 77 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 33 (b) 11 (c) 1 (d) 44
23. 23.Two ribbons are 50 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) 50 cm (b) 5 cm (c) 40 cm (d) 10 cm
24. 24.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) 12 cm (b) 144 cm (c) 6 cm (d) 36 cm
25. 25.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) 336 (c) 40 (d) 168
26. 26.Two ribbons are 10 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) 60 cm (b) 1 cm (c) 2 cm (d) 10 cm
27. 27.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
28. 28.What is the smallest number of sweets that can be shared equally among 6 children or among 14 children, with none left over? (a) 20 (b) 43 (c) 84 (d) 42
29. 29.Two ribbons are 30 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) 1 cm (b) 210 cm (c) 5 cm (d) 30 cm
30. 30.What is the smallest number of sweets that can be shared equally among 10 children or among 14 children, with none left over? (a) 24 (b) 140 (c) 71 (d) 70
31. 31.Two ribbons are 12 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) 3 cm (b) 30 cm (c) 6 cm (d) 12 cm
32. 32.Two ribbons are 20 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) 12 cm (b) 4 cm (c) 2 cm (d) 20 cm
33. 33.A teacher has 24 pencils and 42 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 18 (b) 24 (c) 3 (d) 6
34. 34.What is the smallest number of sweets that can be shared equally among 6 children or among 8 children, with none left over? (a) 25 (b) 24 (c) 48 (d) 14
35. 35.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) 2 cm (c) 6 cm (d) 4 cm
36. 36.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) 5 (d) 20
37. 37.Two ribbons are 8 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) 28 cm (b) 8 cm (c) 4 cm (d) 2 cm
38. 38.A teacher has 49 pencils and 56 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 392 (c) 49 (d) 7
39. 39.Two bells ring every 18 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 3 min (b) 39 min (c) 378 min (d) 126 min
40. 40.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) 360 min (b) 60 min (c) 6 min (d) 42 min

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