HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 84 · 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 49 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) 392 cm (c) 7 cm (d) 49 cm
2. 2.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) 84 min (b) 20 min (c) 2 min (d) 42 min
3. 3.A teacher has 49 pencils and 63 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 7 (c) 14 (d) 49
4. 4.What is the smallest number of sweets that can be shared equally among 6 children or among 21 children, with none left over? (a) 126 (b) 84 (c) 27 (d) 42
5. 5.Two ribbons are 18 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) 3 cm (b) 54 cm (c) 9 cm (d) 18 cm
6. 6.Two ribbons are 24 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) 4 cm (b) 8 cm (c) 24 cm (d) 32 cm
7. 7.A teacher has 72 pencils and 84 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 12 (b) 504 (c) 72 (d) 6
8. 8.Two ribbons are 10 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) 5 cm (b) 1 cm (c) 10 cm (d) 35 cm
9. 9.Two ribbons are 16 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) 24 cm (b) 16 cm (c) 8 cm (d) 4 cm
10. 10.Two bells ring every 10 minutes and every 35 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 350 min (b) 70 min (c) 5 min (d) 45 min
11. 11.A teacher has 35 pencils and 40 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 35 (c) 5 (d) 280
12. 12.Two ribbons are 18 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) 6 cm (b) 18 cm (c) 72 cm (d) 3 cm
13. 13.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) 26 (c) 168 (d) 84
14. 14.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) 216 min (b) 6 min (c) 30 min (d) 36 min
15. 15.What is the smallest number of sweets that can be shared equally among 8 children or among 10 children, with none left over? (a) 41 (b) 80 (c) 40 (d) 18
16. 16.Two bells ring every 25 minutes and every 30 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 750 min (b) 5 min (c) 55 min (d) 150 min
17. 17.A teacher has 12 pencils and 27 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) 12 (d) 3
18. 18.A teacher has 54 pencils and 63 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 9 (b) 3 (c) 378 (d) 54
19. 19.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) 252 (d) 126
20. 20.A teacher has 84 pencils and 96 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 672 (b) 6 (c) 12 (d) 84
21. 21.Two ribbons are 8 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) 4 cm (b) 2 cm (c) 8 cm (d) 20 cm
22. 22.A teacher has 45 pencils and 54 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 270 (c) 9 (d) 45
23. 23.A teacher has 30 pencils and 80 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) 50 (d) 10
24. 24.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) 39 min (d) 126 min
25. 25.Two ribbons are 60 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) 6 cm (b) 36 cm (c) 12 cm (d) 60 cm
26. 26.Two bells ring every 12 minutes and every 15 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 3 min (b) 180 min (c) 60 min (d) 27 min
27. 27.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) 30 cm (b) 5 cm (c) 1 cm (d) 210 cm
28. 28.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) 56 (c) 22 (d) 57
29. 29.A teacher has 6 pencils and 9 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 18 (b) 1 (c) 3 (d) 6
30. 30.What is the smallest number of sweets that can be shared equally among 10 children or among 25 children, with none left over? (a) 35 (b) 100 (c) 50 (d) 250
31. 31.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) 28 (c) 18 (d) 29
32. 32.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) 168 (d) 40
33. 33.What is the smallest number of sweets that can be shared equally among 15 children or among 21 children, with none left over? (a) 36 (b) 210 (c) 105 (d) 315
34. 34.A teacher has 21 pencils and 35 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 7 (b) 21 (c) 14 (d) 1
35. 35.Two ribbons are 24 cm and 108 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) 12 cm (c) 84 cm (d) 6 cm
36. 36.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) 24 min (c) 2 min (d) 14 min
37. 37.Two ribbons are 8 cm and 18 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) 8 cm (c) 2 cm (d) 1 cm
38. 38.Two ribbons are 12 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) 12 cm (b) 6 cm (c) 18 cm (d) 3 cm
39. 39.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) 3 (b) 18 (c) 24 (d) 6
40. 40.A teacher has 16 pencils and 36 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 20 (b) 2 (c) 4 (d) 16

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