HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 588 · 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 20 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) 20 cm (b) 50 cm (c) 10 cm (d) 5 cm
2. 2.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) 2 min (b) 60 min (c) 120 min (d) 22 min
3. 3.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) 28 min (b) 4 min (c) 48 min (d) 192 min
4. 4.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) 4 min (b) 96 min (c) 20 min (d) 24 min
5. 5.Two ribbons are 4 cm and 14 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) 10 cm (d) 1 cm
6. 6.Two ribbons are 6 cm and 14 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) 6 cm (c) 1 cm (d) 2 cm
7. 7.Two ribbons are 21 cm and 27 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 21 cm (b) 1 cm (c) 3 cm (d) 6 cm
8. 8.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) 2 min (c) 80 min (d) 40 min
9. 9.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) 2 (b) 12 (c) 4 (d) 16
10. 10.Two ribbons are 24 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) 24 cm (b) 32 cm (c) 8 cm (d) 4 cm
11. 11.Two bells ring every 12 minutes and every 30 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 360 min (b) 60 min (c) 42 min (d) 6 min
12. 12.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) 61 (c) 120 (d) 60
13. 13.A teacher has 63 pencils and 72 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 504 (b) 63 (c) 3 (d) 9
14. 14.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) 504 min (b) 6 min (c) 54 min (d) 84 min
15. 15.Two bells ring every 18 minutes and every 24 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 432 min (b) 42 min (c) 72 min (d) 6 min
16. 16.Two ribbons are 22 cm and 55 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 22 cm (b) 11 cm (c) 1 cm (d) 33 cm
17. 17.What is the smallest number of sweets that can be shared equally among 16 children or among 20 children, with none left over? (a) 36 (b) 160 (c) 320 (d) 80
18. 18.A teacher has 8 pencils and 10 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 2 (c) 40 (d) 8
19. 19.A teacher has 48 pencils and 56 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 4 (b) 48 (c) 8 (d) 336
20. 20.A teacher has 20 pencils and 24 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) 2 (d) 120
21. 21.Two ribbons are 28 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) 7 cm (b) 1 cm (c) 28 cm (d) 21 cm
22. 22.Two ribbons are 10 cm and 12 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 60 cm (b) 10 cm (c) 1 cm (d) 2 cm
23. 23.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) 6 min (b) 216 min (c) 30 min (d) 36 min
24. 24.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) 48 (c) 24 (d) 20
25. 25.Two ribbons are 10 cm and 14 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) 4 cm (c) 10 cm (d) 2 cm
26. 26.Two ribbons are 18 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) 3 cm (b) 63 cm (c) 18 cm (d) 9 cm
27. 27.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) 30 min (b) 150 min (c) 25 min (d) 5 min
28. 28.What is the smallest number of sweets that can be shared equally among 8 children or among 28 children, with none left over? (a) 36 (b) 224 (c) 56 (d) 112
29. 29.What is the smallest number of sweets that can be shared equally among 10 children or among 15 children, with none left over? (a) 25 (b) 150 (c) 30 (d) 60
30. 30.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) 14 min (b) 2 min (c) 48 min (d) 24 min
31. 31.A teacher has 24 pencils and 40 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 16 (b) 8 (c) 4 (d) 24
32. 32.Two bells ring every 12 minutes and every 20 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 32 min (b) 240 min (c) 60 min (d) 4 min
33. 33.Two bells ring every 9 minutes and every 15 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 45 min (b) 135 min (c) 3 min (d) 24 min
34. 34.Two ribbons are 10 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) 10 cm (b) 8 cm (c) 2 cm (d) 1 cm
35. 35.A teacher has 18 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) 18 (c) 126 (d) 1
36. 36.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) 30 (c) 5 (d) 20
37. 37.Two ribbons are 18 cm and 24 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) 72 cm
38. 38.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) 3 min (b) 270 min (c) 33 min (d) 90 min
39. 39.What is the smallest number of sweets that can be shared equally among 18 children or among 42 children, with none left over? (a) 252 (b) 126 (c) 756 (d) 60
40. 40.Two ribbons are 18 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) 3 cm (c) 18 cm (d) 6 cm

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad