HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 209 · 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 30 pencils and 50 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) 20
2. 2.Two ribbons are 15 cm and 25 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) 10 cm (c) 15 cm (d) 5 cm
3. 3.A teacher has 6 pencils and 21 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 3 (c) 15 (d) 1
4. 4.Two bells ring every 12 minutes and every 42 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 6 min (b) 504 min (c) 54 min (d) 84 min
5. 5.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) 27 min (c) 180 min (d) 60 min
6. 6.What is the smallest number of sweets that can be shared equally among 18 children or among 42 children, with none left over? (a) 60 (b) 756 (c) 252 (d) 126
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) 56 (c) 22 (d) 57
8. 8.Two bells ring every 6 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 3 min (b) 126 min (c) 42 min (d) 27 min
9. 9.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
10. 10.Two ribbons are 54 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) 9 cm (b) 3 cm (c) 54 cm (d) 378 cm
11. 11.Two bells ring every 10 minutes and every 15 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 150 min (b) 5 min (c) 25 min (d) 30 min
12. 12.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) 72 (b) 12 (c) 24 (d) 6
13. 13.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
14. 14.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) 6 cm (c) 12 cm (d) 30 cm
15. 15.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) 39 min (c) 3 min (d) 126 min
16. 16.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) 54 (c) 378 (d) 3
17. 17.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) 8 (b) 6 (c) 2 (d) 1
18. 18.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) 5 (b) 1 (c) 35 (d) 280
19. 19.A teacher has 24 pencils and 64 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 4 (b) 40 (c) 8 (d) 24
20. 20.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) 10 cm (b) 5 cm (c) 40 cm (d) 50 cm
21. 21.A teacher has 84 pencils and 108 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 24 (b) 12 (c) 84 (d) 6
22. 22.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) 168 min (c) 26 min (d) 84 min
23. 23.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) 2 min (b) 140 min (c) 70 min (d) 24 min
24. 24.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) 54 min (b) 15 min (c) 3 min (d) 18 min
25. 25.Two ribbons are 15 cm and 20 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 15 cm (b) 1 cm (c) 60 cm (d) 5 cm
26. 26.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) 1 (c) 22 (d) 11
27. 27.A teacher has 16 pencils and 28 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 16 (b) 4 (c) 2 (d) 12
28. 28.A teacher has 28 pencils and 36 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 8 (b) 4 (c) 2 (d) 28
29. 29.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) 105 min (b) 5 min (c) 525 min (d) 50 min
30. 30.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) 8 cm (c) 2 cm (d) 20 cm
31. 31.Two bells ring every 8 minutes and every 28 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 36 min (b) 4 min (c) 224 min (d) 56 min
32. 32.What is the smallest number of sweets that can be shared equally among 9 children or among 15 children, with none left over? (a) 90 (b) 135 (c) 24 (d) 45
33. 33.Two ribbons are 44 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) 33 cm (b) 1 cm (c) 11 cm (d) 44 cm
34. 34.What is the smallest number of sweets that can be shared equally among 20 children or among 28 children, with none left over? (a) 560 (b) 280 (c) 48 (d) 140
35. 35.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) 84 cm (b) 12 cm (c) 672 cm (d) 6 cm
36. 36.Two bells ring every 12 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 33 min (b) 3 min (c) 84 min (d) 252 min
37. 37.Two ribbons are 12 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) 2 cm (c) 4 cm (d) 20 cm
38. 38.What is the smallest number of sweets that can be shared equally among 4 children or among 6 children, with none left over? (a) 24 (b) 10 (c) 12 (d) 13
39. 39.A teacher has 21 pencils and 56 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) 1 (d) 35
40. 40.What is the smallest number of sweets that can be shared equally among 20 children or among 24 children, with none left over? (a) 44 (b) 120 (c) 240 (d) 480

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