HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 368 · 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 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) 252 min (b) 3 min (c) 33 min (d) 84 min
2. 2.Two ribbons are 72 cm and 81 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 72 cm (b) 9 cm (c) 3 cm (d) 648 cm
3. 3.What is the smallest number of sweets that can be shared equally among 8 children or among 28 children, with none left over? (a) 224 (b) 112 (c) 56 (d) 36
4. 4.Two bells ring every 4 minutes and every 6 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 12 min (b) 2 min (c) 24 min (d) 10 min
5. 5.Two ribbons are 12 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) 3 cm (b) 36 cm (c) 6 cm (d) 12 cm
6. 6.A teacher has 8 pencils and 14 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 2 (b) 6 (c) 1 (d) 8
7. 7.A teacher has 24 pencils and 54 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 24 (b) 3 (c) 30 (d) 6
8. 8.What is the smallest number of sweets that can be shared equally among 8 children or among 14 children, with none left over? (a) 22 (b) 56 (c) 112 (d) 57
9. 9.What is the smallest number of sweets that can be shared equally among 9 children or among 21 children, with none left over? (a) 63 (b) 126 (c) 30 (d) 189
10. 10.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) 30 cm (c) 5 cm (d) 40 cm
11. 11.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) 20 (b) 5 (c) 70 (d) 10
12. 12.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) 6 cm (c) 672 cm (d) 12 cm
13. 13.Two ribbons are 21 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) 28 cm (b) 7 cm (c) 21 cm (d) 1 cm
14. 14.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
15. 15.What is the smallest number of sweets that can be shared equally among 15 children or among 25 children, with none left over? (a) 75 (b) 40 (c) 375 (d) 150
16. 16.Two ribbons are 36 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) 27 cm (d) 36 cm
17. 17.Two ribbons are 6 cm and 9 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) 1 cm (c) 18 cm (d) 6 cm
18. 18.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) 5 min (b) 35 min (c) 50 min (d) 250 min
19. 19.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) 84 (c) 168 (d) 40
20. 20.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) 28 (b) 2 (c) 4 (d) 8
21. 21.A teacher has 9 pencils and 24 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 15 (c) 9 (d) 1
22. 22.A teacher has 16 pencils and 20 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) 80 (d) 2
23. 23.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) 330 (b) 11 (c) 1 (d) 55
24. 24.What is the smallest number of sweets that can be shared equally among 20 children or among 25 children, with none left over? (a) 200 (b) 500 (c) 100 (d) 45
25. 25.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
26. 26.Two bells ring every 12 minutes and every 16 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 192 min (b) 4 min (c) 48 min (d) 28 min
27. 27.Two bells ring every 4 minutes and every 10 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 20 min (b) 2 min (c) 14 min (d) 40 min
28. 28.A teacher has 24 pencils and 60 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 24 (b) 6 (c) 36 (d) 12
29. 29.Two ribbons are 6 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) 6 cm (b) 1 cm (c) 4 cm (d) 2 cm
30. 30.Two bells ring every 12 minutes and every 28 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 336 min (b) 4 min (c) 84 min (d) 40 min
31. 31.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) 112 (d) 224
32. 32.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) 70 min (b) 2 min (c) 140 min (d) 24 min
33. 33.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) 49 cm (c) 7 cm (d) 1 cm
34. 34.A teacher has 16 pencils and 72 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 56 (b) 8 (c) 4 (d) 16
35. 35.Two bells ring every 16 minutes and every 28 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 112 min (b) 44 min (c) 4 min (d) 448 min
36. 36.What is the smallest number of sweets that can be shared equally among 4 children or among 6 children, with none left over? (a) 10 (b) 12 (c) 13 (d) 24
37. 37.A teacher has 6 pencils and 16 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 1 (c) 2 (d) 10
38. 38.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) 40 cm (c) 10 cm (d) 5 cm
39. 39.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) 150 min (b) 5 min (c) 55 min (d) 750 min
40. 40.Two ribbons are 48 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) 6 cm (b) 60 cm (c) 48 cm (d) 12 cm

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