HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 589 · 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 48 cm and 84 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) 48 cm (c) 36 cm (d) 6 cm
2. 2.What is the smallest number of sweets that can be shared equally among 25 children or among 30 children, with none left over? (a) 55 (b) 750 (c) 150 (d) 300
3. 3.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) 3 min (b) 378 min (c) 39 min (d) 126 min
4. 4.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) 25 min (c) 150 min (d) 5 min
5. 5.Two ribbons are 44 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) 1 cm (b) 44 cm (c) 220 cm (d) 11 cm
6. 6.Two bells ring every 18 minutes and every 42 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 6 min (b) 126 min (c) 756 min (d) 60 min
7. 7.Two ribbons are 24 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) 8 cm (b) 4 cm (c) 24 cm (d) 96 cm
8. 8.What is the smallest number of sweets that can be shared equally among 20 children or among 25 children, with none left over? (a) 45 (b) 200 (c) 500 (d) 100
9. 9.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) 90 min (c) 3 min (d) 33 min
10. 10.Two ribbons are 16 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) 4 cm (b) 8 cm (c) 48 cm (d) 16 cm
11. 11.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
12. 12.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) 48 min (c) 4 min (d) 28 min
13. 13.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) 2 min (b) 56 min (c) 22 min (d) 112 min
14. 14.What is the smallest number of sweets that can be shared equally among 15 children or among 20 children, with none left over? (a) 300 (b) 120 (c) 35 (d) 60
15. 15.Two ribbons are 18 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) 54 cm (b) 3 cm (c) 18 cm (d) 9 cm
16. 16.A teacher has 16 pencils and 18 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 144 (c) 16 (d) 2
17. 17.Two ribbons are 35 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) 280 cm (b) 5 cm (c) 35 cm (d) 1 cm
18. 18.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
19. 19.Two ribbons are 20 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) 16 cm (b) 4 cm (c) 2 cm (d) 20 cm
20. 20.Two bells ring every 15 minutes and every 35 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 5 min (b) 525 min (c) 50 min (d) 105 min
21. 21.What is the smallest number of sweets that can be shared equally among 6 children or among 9 children, with none left over? (a) 36 (b) 15 (c) 18 (d) 54
22. 22.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) 500 min (b) 5 min (c) 100 min (d) 45 min
23. 23.What is the smallest number of sweets that can be shared equally among 18 children or among 30 children, with none left over? (a) 90 (b) 180 (c) 48 (d) 540
24. 24.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) 15 min (b) 54 min (c) 18 min (d) 3 min
25. 25.What is the smallest number of sweets that can be shared equally among 18 children or among 24 children, with none left over? (a) 432 (b) 144 (c) 42 (d) 72
26. 26.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) 60 (c) 12 (d) 36
27. 27.What is the smallest number of sweets that can be shared equally among 8 children or among 12 children, with none left over? (a) 24 (b) 48 (c) 20 (d) 96
28. 28.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) 2 (c) 1 (d) 4
29. 29.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) 240 min (b) 4 min (c) 32 min (d) 60 min
30. 30.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) 12 cm (b) 48 cm (c) 6 cm (d) 60 cm
31. 31.Two ribbons are 56 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) 8 cm (b) 56 cm (c) 16 cm (d) 4 cm
32. 32.Two ribbons are 20 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) 10 cm (b) 5 cm (c) 20 cm (d) 60 cm
33. 33.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) 18 min (b) 28 min (c) 2 min (d) 56 min
34. 34.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) 4 min (b) 112 min (c) 448 min (d) 44 min
35. 35.A teacher has 12 pencils and 20 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 4 (b) 2 (c) 12 (d) 8
36. 36.What is the smallest number of sweets that can be shared equally among 4 children or among 14 children, with none left over? (a) 28 (b) 18 (c) 56 (d) 29
37. 37.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) 44 cm (b) 11 cm (c) 55 cm (d) 1 cm
38. 38.A teacher has 35 pencils and 42 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 35 (c) 7 (d) 210
39. 39.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) 1 cm (b) 6 cm (c) 8 cm (d) 2 cm
40. 40.Two ribbons are 10 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) 1 cm (b) 5 cm (c) 35 cm (d) 10 cm

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