HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 240 · 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 27 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) 45 cm (b) 27 cm (c) 9 cm (d) 3 cm
2. 2.A teacher has 4 pencils and 6 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) 4 (d) 2
3. 3.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) 7 cm (b) 14 cm (c) 1 cm (d) 49 cm
4. 4.Two ribbons are 44 cm and 99 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) 44 cm (c) 55 cm (d) 11 cm
5. 5.Two ribbons are 12 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) 4 cm (b) 2 cm (c) 48 cm (d) 12 cm
6. 6.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) 45 min (b) 500 min (c) 100 min (d) 5 min
7. 7.A teacher has 20 pencils and 50 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 10 (b) 5 (c) 30 (d) 20
8. 8.A teacher has 77 pencils and 88 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 11 (b) 77 (c) 1 (d) 616
9. 9.A teacher has 15 pencils and 21 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 6 (c) 1 (d) 15
10. 10.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) 12 (c) 13 (d) 10
11. 11.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) 270 min (b) 33 min (c) 90 min (d) 3 min
12. 12.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) 108 min (b) 36 min (c) 3 min (d) 21 min
13. 13.A teacher has 8 pencils and 28 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 20 (b) 4 (c) 8 (d) 2
14. 14.What is the smallest number of sweets that can be shared equally among 6 children or among 9 children, with none left over? (a) 18 (b) 15 (c) 54 (d) 36
15. 15.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) 504 cm (b) 63 cm (c) 9 cm (d) 3 cm
16. 16.What is the smallest number of sweets that can be shared equally among 8 children or among 14 children, with none left over? (a) 57 (b) 22 (c) 112 (d) 56
17. 17.Two ribbons are 22 cm and 33 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 66 cm (b) 1 cm (c) 11 cm (d) 22 cm
18. 18.Two ribbons are 27 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) 3 cm (b) 9 cm (c) 36 cm (d) 27 cm
19. 19.Two ribbons are 20 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) 20 cm (b) 12 cm (c) 4 cm (d) 2 cm
20. 20.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) 40 min (b) 160 min (c) 28 min (d) 4 min
21. 21.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) 54 min (c) 15 min (d) 18 min
22. 22.What is the smallest number of sweets that can be shared equally among 18 children or among 21 children, with none left over? (a) 252 (b) 126 (c) 39 (d) 378
23. 23.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
24. 24.What is the smallest number of sweets that can be shared equally among 12 children or among 14 children, with none left over? (a) 26 (b) 84 (c) 85 (d) 168
25. 25.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) 378 cm (c) 54 cm (d) 3 cm
26. 26.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) 24 min (b) 2 min (c) 48 min (d) 14 min
27. 27.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
28. 28.Two bells ring every 15 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 315 min (b) 105 min (c) 36 min (d) 3 min
29. 29.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) 60 (b) 12 (c) 36 (d) 6
30. 30.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) 18 min (b) 40 min (c) 2 min (d) 80 min
31. 31.Two ribbons are 21 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) 1 cm (b) 84 cm (c) 21 cm (d) 7 cm
32. 32.A teacher has 33 pencils and 88 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 55 (b) 33 (c) 1 (d) 11
33. 33.What is the smallest number of sweets that can be shared equally among 10 children or among 15 children, with none left over? (a) 150 (b) 30 (c) 60 (d) 25
34. 34.A teacher has 9 pencils and 15 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) 9 (d) 3
35. 35.A teacher has 44 pencils and 77 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 44 (c) 11 (d) 33
36. 36.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) 40 min (b) 14 min (c) 2 min (d) 20 min
37. 37.Two ribbons are 12 cm and 21 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) 3 cm (c) 9 cm (d) 1 cm
38. 38.Two bells ring every 9 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 30 min (b) 63 min (c) 189 min (d) 3 min
39. 39.What is the smallest number of sweets that can be shared equally among 15 children or among 35 children, with none left over? (a) 525 (b) 50 (c) 105 (d) 210
40. 40.Two bells ring every 20 minutes and every 28 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 560 min (b) 48 min (c) 140 min (d) 4 min

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