HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 460 · 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.Two ribbons are 35 cm and 56 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) 35 cm (d) 7 cm
2. 2.Two ribbons are 14 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) 14 cm (b) 7 cm (c) 49 cm (d) 1 cm
3. 3.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) 5 min (c) 40 min (d) 375 min
4. 4.Two ribbons are 56 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) 56 cm (b) 7 cm (c) 1 cm (d) 504 cm
5. 5.What is the smallest number of sweets that can be shared equally among 15 children or among 35 children, with none left over? (a) 50 (b) 210 (c) 525 (d) 105
6. 6.Two ribbons are 21 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) 14 cm (c) 7 cm (d) 21 cm
7. 7.Two ribbons are 27 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) 27 cm (b) 18 cm (c) 9 cm (d) 3 cm
8. 8.What is the smallest number of sweets that can be shared equally among 16 children or among 20 children, with none left over? (a) 160 (b) 320 (c) 80 (d) 36
9. 9.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) 30 (b) 10 (c) 5 (d) 1
10. 10.Two bells ring every 8 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 112 min (b) 2 min (c) 22 min (d) 56 min
11. 11.What is the smallest number of sweets that can be shared equally among 6 children or among 8 children, with none left over? (a) 24 (b) 14 (c) 25 (d) 48
12. 12.Two ribbons are 18 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) 18 cm (b) 24 cm (c) 6 cm (d) 3 cm
13. 13.A teacher has 70 pencils and 90 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 70 (b) 5 (c) 10 (d) 20
14. 14.Two ribbons are 24 cm and 54 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) 3 cm (c) 24 cm (d) 30 cm
15. 15.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) 30 min (b) 36 min (c) 6 min (d) 216 min
16. 16.A teacher has 16 pencils and 18 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 16 (c) 2 (d) 144
17. 17.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) 3 (b) 30 (c) 12 (d) 6
18. 18.A teacher has 27 pencils and 45 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 27 (b) 9 (c) 3 (d) 18
19. 19.A teacher has 44 pencils and 77 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 33 (c) 11 (d) 44
20. 20.Two ribbons are 24 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) 12 cm (b) 6 cm (c) 24 cm (d) 36 cm
21. 21.Two ribbons are 21 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) 21 cm (b) 1 cm (c) 6 cm (d) 3 cm
22. 22.What is the smallest number of sweets that can be shared equally among 10 children or among 35 children, with none left over? (a) 70 (b) 140 (c) 350 (d) 45
23. 23.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) 378 min (b) 3 min (c) 126 min (d) 39 min
24. 24.What is the smallest number of sweets that can be shared equally among 4 children or among 14 children, with none left over? (a) 18 (b) 29 (c) 28 (d) 56
25. 25.What is the smallest number of sweets that can be shared equally among 12 children or among 14 children, with none left over? (a) 85 (b) 168 (c) 26 (d) 84
26. 26.Two bells ring every 6 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 2 min (b) 20 min (c) 42 min (d) 84 min
27. 27.A teacher has 35 pencils and 45 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 35 (b) 1 (c) 10 (d) 5
28. 28.What is the smallest number of sweets that can be shared equally among 6 children or among 15 children, with none left over? (a) 30 (b) 60 (c) 90 (d) 21
29. 29.A teacher has 42 pencils and 48 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 336 (c) 6 (d) 42
30. 30.What is the smallest number of sweets that can be shared equally among 16 children or among 28 children, with none left over? (a) 448 (b) 44 (c) 224 (d) 112
31. 31.Two ribbons are 28 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) 35 cm (b) 1 cm (c) 28 cm (d) 7 cm
32. 32.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) 48 (c) 20 (d) 24
33. 33.What is the smallest number of sweets that can be shared equally among 15 children or among 20 children, with none left over? (a) 120 (b) 35 (c) 60 (d) 300
34. 34.Two ribbons are 24 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) 24 cm (b) 72 cm (c) 12 cm (d) 6 cm
35. 35.Two ribbons are 8 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) 2 cm (b) 40 cm (c) 8 cm (d) 1 cm
36. 36.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) 22 min (b) 60 min (c) 2 min (d) 120 min
37. 37.A teacher has 24 pencils and 40 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 24 (b) 16 (c) 8 (d) 4
38. 38.What is the smallest number of sweets that can be shared equally among 12 children or among 42 children, with none left over? (a) 168 (b) 54 (c) 84 (d) 504
39. 39.What is the smallest number of sweets that can be shared equally among 18 children or among 21 children, with none left over? (a) 378 (b) 39 (c) 126 (d) 252
40. 40.Two ribbons are 25 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) 25 cm (b) 1 cm (c) 5 cm (d) 15 cm

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