HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 396 · 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.A teacher has 50 pencils and 80 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) 30 (d) 10
2. 2.Two bells ring every 6 minutes and every 15 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 21 min (b) 3 min (c) 30 min (d) 90 min
3. 3.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) 9 cm (b) 1 cm (c) 12 cm (d) 3 cm
4. 4.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
5. 5.A teacher has 12 pencils and 18 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 36 (b) 3 (c) 12 (d) 6
6. 6.What is the smallest number of sweets that can be shared equally among 12 children or among 20 children, with none left over? (a) 240 (b) 120 (c) 60 (d) 32
7. 7.A teacher has 25 pencils and 30 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 5 (c) 150 (d) 25
8. 8.What is the smallest number of sweets that can be shared equally among 6 children or among 10 children, with none left over? (a) 31 (b) 16 (c) 30 (d) 60
9. 9.Two ribbons are 44 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) 1 cm (b) 33 cm (c) 11 cm (d) 44 cm
10. 10.What is the smallest number of sweets that can be shared equally among 8 children or among 28 children, with none left over? (a) 112 (b) 56 (c) 224 (d) 36
11. 11.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
12. 12.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) 16 (b) 4 (c) 2 (d) 12
13. 13.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) 29 (c) 56 (d) 18
14. 14.A teacher has 16 pencils and 24 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 48 (b) 4 (c) 16 (d) 8
15. 15.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) 192 min (d) 48 min
16. 16.What is the smallest number of sweets that can be shared equally among 8 children or among 10 children, with none left over? (a) 40 (b) 41 (c) 18 (d) 80
17. 17.What is the smallest number of sweets that can be shared equally among 8 children or among 20 children, with none left over? (a) 80 (b) 28 (c) 160 (d) 40
18. 18.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
19. 19.What is the smallest number of sweets that can be shared equally among 6 children or among 15 children, with none left over? (a) 30 (b) 21 (c) 90 (d) 60
20. 20.What is the smallest number of sweets that can be shared equally among 4 children or among 10 children, with none left over? (a) 21 (b) 20 (c) 14 (d) 40
21. 21.Two ribbons are 10 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) 10 cm (c) 6 cm (d) 2 cm
22. 22.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) 6 cm (c) 12 cm (d) 3 cm
23. 23.What is the smallest number of sweets that can be shared equally among 15 children or among 25 children, with none left over? (a) 75 (b) 375 (c) 150 (d) 40
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) 54 min (b) 3 min (c) 15 min (d) 18 min
25. 25.Two ribbons are 24 cm and 64 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 40 cm (b) 4 cm (c) 24 cm (d) 8 cm
26. 26.Two ribbons are 35 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) 35 cm (b) 7 cm (c) 14 cm (d) 1 cm
27. 27.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) 28 min (b) 56 min (c) 2 min (d) 18 min
28. 28.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) 8 (c) 40 (d) 2
29. 29.What is the smallest number of sweets that can be shared equally among 6 children or among 14 children, with none left over? (a) 42 (b) 43 (c) 20 (d) 84
30. 30.What is the smallest number of sweets that can be shared equally among 12 children or among 18 children, with none left over? (a) 30 (b) 72 (c) 36 (d) 216
31. 31.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) 4 min (b) 28 min (c) 160 min (d) 40 min
32. 32.A teacher has 24 pencils and 84 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 12 (b) 60 (c) 24 (d) 6
33. 33.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) 48 cm (b) 12 cm (c) 6 cm (d) 60 cm
34. 34.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) 60 min (c) 240 min (d) 4 min
35. 35.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) 26 min (b) 168 min (c) 2 min (d) 84 min
36. 36.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) 11 cm (b) 1 cm (c) 22 cm (d) 66 cm
37. 37.Two ribbons are 9 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) 9 cm (c) 15 cm (d) 1 cm
38. 38.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) 84 min (b) 2 min (c) 20 min (d) 42 min
39. 39.Two bells ring every 10 minutes and every 25 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 35 min (b) 5 min (c) 250 min (d) 50 min
40. 40.A teacher has 12 pencils and 54 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 12 (b) 6 (c) 42 (d) 3

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