HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 86 · 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 12 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) 16 cm (b) 2 cm (c) 4 cm (d) 12 cm
2. 2.A teacher has 45 pencils and 63 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 9 (b) 45 (c) 3 (d) 18
3. 3.Two ribbons are 15 cm and 25 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 15 cm (b) 5 cm (c) 10 cm (d) 1 cm
4. 4.What is the smallest number of sweets that can be shared equally among 15 children or among 18 children, with none left over? (a) 270 (b) 90 (c) 180 (d) 33
5. 5.A teacher has 36 pencils and 63 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 36 (c) 9 (d) 27
6. 6.What is the smallest number of sweets that can be shared equally among 9 children or among 21 children, with none left over? (a) 126 (b) 63 (c) 189 (d) 30
7. 7.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) 22 min (b) 112 min (c) 2 min (d) 56 min
8. 8.Two ribbons are 30 cm and 50 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) 30 cm
9. 9.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) 2 (b) 8 (c) 40 (d) 1
10. 10.Two ribbons are 20 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) 5 cm (b) 20 cm (c) 70 cm (d) 10 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) 6 min (b) 42 min (c) 60 min (d) 360 min
12. 12.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) 24 min (c) 2 min (d) 48 min
13. 13.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) 24 (c) 13 (d) 12
14. 14.Two bells ring every 16 minutes and every 20 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 4 min (b) 80 min (c) 36 min (d) 320 min
15. 15.What is the smallest number of sweets that can be shared equally among 6 children or among 21 children, with none left over? (a) 42 (b) 27 (c) 84 (d) 126
16. 16.Two bells ring every 12 minutes and every 15 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 3 min (b) 27 min (c) 180 min (d) 60 min
17. 17.Two ribbons are 6 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) 3 cm (b) 21 cm (c) 6 cm (d) 1 cm
18. 18.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) 10 min (b) 2 min (c) 24 min (d) 12 min
19. 19.What is the smallest number of sweets that can be shared equally among 10 children or among 12 children, with none left over? (a) 120 (b) 61 (c) 22 (d) 60
20. 20.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) 2 (c) 80 (d) 4
21. 21.What is the smallest number of sweets that can be shared equally among 12 children or among 15 children, with none left over? (a) 60 (b) 180 (c) 120 (d) 27
22. 22.Two ribbons are 32 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) 32 cm (b) 40 cm (c) 8 cm (d) 4 cm
23. 23.What is the smallest number of sweets that can be shared equally among 9 children or among 12 children, with none left over? (a) 36 (b) 108 (c) 21 (d) 72
24. 24.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) 80 min (d) 2 min
25. 25.What is the smallest number of sweets that can be shared equally among 15 children or among 25 children, with none left over? (a) 375 (b) 150 (c) 40 (d) 75
26. 26.A teacher has 40 pencils and 72 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 8 (b) 40 (c) 32 (d) 4
27. 27.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) 72 (c) 42 (d) 144
28. 28.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) 40 min (d) 84 min
29. 29.Two ribbons are 30 cm and 35 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 5 cm (b) 1 cm (c) 30 cm (d) 210 cm
30. 30.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) 36 min (b) 108 min (c) 21 min (d) 3 min
31. 31.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) 21 cm (b) 1 cm (c) 7 cm (d) 28 cm
32. 32.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) 39 (c) 378 (d) 126
33. 33.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) 1 cm (b) 6 cm (c) 2 cm (d) 4 cm
34. 34.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) 9 (b) 63 (c) 3 (d) 504
35. 35.Two bells ring every 6 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 2 min (b) 20 min (c) 84 min (d) 42 min
36. 36.Two ribbons are 12 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) 84 cm (b) 12 cm (c) 1 cm (d) 2 cm
37. 37.Two ribbons are 42 cm and 54 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 42 cm (b) 3 cm (c) 12 cm (d) 6 cm
38. 38.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) 4 min (b) 48 min (c) 28 min (d) 192 min
39. 39.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
40. 40.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) 11 (c) 330 (d) 55

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