HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 613 · 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 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) 4 cm (d) 8 cm
2. 2.A teacher has 14 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
3. 3.A teacher has 36 pencils and 45 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 36 (b) 180 (c) 9 (d) 3
4. 4.What is the smallest number of sweets that can be shared equally among 10 children or among 25 children, with none left over? (a) 100 (b) 250 (c) 35 (d) 50
5. 5.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) 56 min (b) 22 min (c) 2 min (d) 112 min
6. 6.Two ribbons are 30 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) 3 cm (b) 18 cm (c) 30 cm (d) 6 cm
7. 7.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) 120 min (b) 60 min (c) 2 min (d) 22 min
8. 8.Two ribbons are 14 cm and 49 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) 14 cm (c) 7 cm (d) 1 cm
9. 9.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) 6 (b) 42 (c) 336 (d) 3
10. 10.A teacher has 24 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) 24 (c) 216 (d) 3
11. 11.What is the smallest number of sweets that can be shared equally among 18 children or among 21 children, with none left over? (a) 126 (b) 252 (c) 39 (d) 378
12. 12.Two bells ring every 10 minutes and every 25 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 50 min (b) 35 min (c) 5 min (d) 250 min
13. 13.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) 48 (c) 14 (d) 24
14. 14.Two ribbons are 30 cm and 50 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) 10 cm (c) 5 cm (d) 30 cm
15. 15.What is the smallest number of sweets that can be shared equally among 20 children or among 35 children, with none left over? (a) 280 (b) 140 (c) 700 (d) 55
16. 16.Two ribbons are 50 cm and 70 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) 20 cm (c) 5 cm (d) 50 cm
17. 17.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) 84 min (d) 42 min
18. 18.What is the smallest number of sweets that can be shared equally among 6 children or among 21 children, with none left over? (a) 84 (b) 126 (c) 27 (d) 42
19. 19.Two bells ring every 24 minutes and every 30 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 54 min (b) 720 min (c) 6 min (d) 120 min
20. 20.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) 24 (c) 135 (d) 45
21. 21.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) 140 min (b) 2 min (c) 70 min (d) 24 min
22. 22.Two bells ring every 9 minutes and every 12 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 3 min (b) 21 min (c) 108 min (d) 36 min
23. 23.A teacher has 25 pencils and 30 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 150 (b) 5 (c) 25 (d) 1
24. 24.Two ribbons are 40 cm and 70 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) 30 cm (d) 40 cm
25. 25.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) 30 min (c) 5 min (d) 25 min
26. 26.A teacher has 9 pencils and 21 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 12 (b) 1 (c) 9 (d) 3
27. 27.A teacher has 35 pencils and 56 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 21 (b) 7 (c) 35 (d) 1
28. 28.Two ribbons are 63 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) 3 cm (b) 63 cm (c) 504 cm (d) 9 cm
29. 29.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) 6 cm (d) 672 cm
30. 30.What is the smallest number of sweets that can be shared equally among 12 children or among 28 children, with none left over? (a) 336 (b) 40 (c) 84 (d) 168
31. 31.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) 18 cm (c) 3 cm (d) 6 cm
32. 32.Two ribbons are 16 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) 16 cm (b) 40 cm (c) 4 cm (d) 8 cm
33. 33.Two ribbons are 24 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) 8 cm (b) 24 cm (c) 4 cm (d) 16 cm
34. 34.Two bells ring every 20 minutes and every 25 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 100 min (b) 500 min (c) 45 min (d) 5 min
35. 35.Two ribbons are 6 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) 10 cm (b) 2 cm (c) 1 cm (d) 6 cm
36. 36.What is the smallest number of sweets that can be shared equally among 10 children or among 12 children, with none left over? (a) 22 (b) 60 (c) 61 (d) 120
37. 37.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) 5 min (c) 45 min (d) 70 min
38. 38.A teacher has 32 pencils and 40 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 160 (b) 32 (c) 4 (d) 8
39. 39.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) 42 min (b) 126 min (c) 27 min (d) 3 min
40. 40.A teacher has 33 pencils and 44 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) 132

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