HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 471 · 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 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) 18 cm (b) 3 cm (c) 1 cm (d) 6 cm
2. 2.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) 6 min (c) 36 min (d) 216 min
3. 3.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) 20 (c) 24 (d) 48
4. 4.Two bells ring every 8 minutes and every 10 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 80 min (b) 40 min (c) 18 min (d) 2 min
5. 5.Two bells ring every 6 minutes and every 10 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 2 min (b) 16 min (c) 60 min (d) 30 min
6. 6.What is the smallest number of sweets that can be shared equally among 12 children or among 18 children, with none left over? (a) 216 (b) 30 (c) 36 (d) 72
7. 7.A teacher has 14 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) 49 (d) 14
8. 8.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) 1 (b) 330 (c) 55 (d) 11
9. 9.A teacher has 18 pencils and 42 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 18 (b) 24 (c) 3 (d) 6
10. 10.Two ribbons are 8 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) 28 cm (b) 4 cm (c) 8 cm (d) 2 cm
11. 11.Two bells ring every 15 minutes and every 20 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 60 min (b) 5 min (c) 300 min (d) 35 min
12. 12.Two ribbons are 6 cm and 8 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) 6 cm (c) 24 cm (d) 2 cm
13. 13.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) 56 (c) 112 (d) 36
14. 14.Two bells ring every 4 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 2 min (b) 18 min (c) 28 min (d) 56 min
15. 15.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) 40 min (b) 336 min (c) 84 min (d) 4 min
16. 16.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) 84 min (b) 26 min (c) 2 min (d) 168 min
17. 17.Two bells ring every 20 minutes and every 24 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 4 min (b) 120 min (c) 480 min (d) 44 min
18. 18.A teacher has 60 pencils and 96 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 36 (c) 60 (d) 12
19. 19.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) 2 min (b) 14 min (c) 24 min (d) 48 min
20. 20.A teacher has 4 pencils and 18 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 14 (b) 4 (c) 1 (d) 2
21. 21.Two bells ring every 8 minutes and every 12 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 20 min (b) 96 min (c) 24 min (d) 4 min
22. 22.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) 36 cm (d) 27 cm
23. 23.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
24. 24.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) 54 min (b) 6 min (c) 84 min (d) 504 min
25. 25.Two ribbons are 22 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) 55 cm (b) 22 cm (c) 11 cm (d) 1 cm
26. 26.Two bells ring every 20 minutes and every 35 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 700 min (b) 5 min (c) 55 min (d) 140 min
27. 27.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) 6 cm (c) 18 cm (d) 30 cm
28. 28.Two ribbons are 50 cm and 80 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) 50 cm (d) 5 cm
29. 29.A teacher has 40 pencils and 90 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 50 (b) 5 (c) 10 (d) 40
30. 30.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) 1 (b) 6 (c) 2 (d) 10
31. 31.What is the smallest number of sweets that can be shared equally among 9 children or among 15 children, with none left over? (a) 135 (b) 90 (c) 24 (d) 45
32. 32.Two ribbons are 28 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) 8 cm (b) 4 cm (c) 28 cm (d) 2 cm
33. 33.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) 3 min (b) 15 min (c) 54 min (d) 18 min
34. 34.Two ribbons are 20 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) 20 cm (b) 1 cm (c) 5 cm (d) 25 cm
35. 35.Two bells ring every 8 minutes and every 20 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 28 min (b) 4 min (c) 40 min (d) 160 min
36. 36.A teacher has 55 pencils and 88 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) 55 (d) 1
37. 37.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) 39 (c) 252 (d) 378
38. 38.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) 1 cm (b) 6 cm (c) 2 cm (d) 10 cm
39. 39.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) 48 min (b) 4 min (c) 28 min (d) 192 min
40. 40.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) 1 (b) 9 (c) 3 (d) 12

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