HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 571 · 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.What is the smallest number of sweets that can be shared equally among 12 children or among 42 children, with none left over? (a) 54 (b) 504 (c) 84 (d) 168
2. 2.Two ribbons are 77 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) 22 cm (b) 1 cm (c) 77 cm (d) 11 cm
3. 3.Two bells ring every 8 minutes and every 28 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 4 min (b) 36 min (c) 224 min (d) 56 min
4. 4.Two ribbons are 15 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) 12 cm (b) 3 cm (c) 15 cm (d) 1 cm
5. 5.A teacher has 36 pencils and 60 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 36 (b) 6 (c) 12 (d) 24
6. 6.Two ribbons are 35 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) 35 cm (b) 5 cm (c) 1 cm (d) 10 cm
7. 7.Two bells ring every 15 minutes and every 20 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 5 min (b) 35 min (c) 300 min (d) 60 min
8. 8.What is the smallest number of sweets that can be shared equally among 12 children or among 18 children, with none left over? (a) 72 (b) 36 (c) 216 (d) 30
9. 9.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) 2 min (c) 56 min (d) 28 min
10. 10.What is the smallest number of sweets that can be shared equally among 10 children or among 25 children, with none left over? (a) 35 (b) 250 (c) 100 (d) 50
11. 11.What is the smallest number of sweets that can be shared equally among 15 children or among 20 children, with none left over? (a) 120 (b) 35 (c) 60 (d) 300
12. 12.Two ribbons are 14 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) 7 cm (b) 42 cm (c) 14 cm (d) 1 cm
13. 13.A teacher has 12 pencils and 15 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 60 (b) 1 (c) 3 (d) 12
14. 14.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) 189 min (b) 3 min (c) 30 min (d) 63 min
15. 15.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) 45 min (d) 100 min
16. 16.What is the smallest number of sweets that can be shared equally among 12 children or among 21 children, with none left over? (a) 33 (b) 84 (c) 252 (d) 168
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) 1 cm (b) 11 cm (c) 22 cm (d) 66 cm
18. 18.A teacher has 22 pencils and 33 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 66 (b) 11 (c) 1 (d) 22
19. 19.Two bells ring every 20 minutes and every 24 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 4 min (b) 120 min (c) 44 min (d) 480 min
20. 20.Two ribbons are 60 cm and 96 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 6 cm (b) 36 cm (c) 60 cm (d) 12 cm
21. 21.Two ribbons are 16 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) 16 cm (b) 56 cm (c) 8 cm (d) 4 cm
22. 22.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) 18 cm (b) 6 cm (c) 3 cm (d) 72 cm
23. 23.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) 60 min (b) 126 min (c) 756 min (d) 6 min
24. 24.A teacher has 64 pencils and 72 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 64 (b) 576 (c) 4 (d) 8
25. 25.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
26. 26.A teacher has 33 pencils and 55 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 33 (b) 1 (c) 22 (d) 11
27. 27.A teacher has 12 pencils and 16 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 12 (b) 48 (c) 4 (d) 2
28. 28.Two ribbons are 20 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) 25 cm (b) 1 cm (c) 20 cm (d) 5 cm
29. 29.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) 3 min (d) 21 min
30. 30.A teacher has 20 pencils and 35 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) 20 (d) 15
31. 31.A teacher has 8 pencils and 12 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 4 (b) 24 (c) 8 (d) 2
32. 32.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) 50 min (b) 105 min (c) 5 min (d) 525 min
33. 33.A teacher has 12 pencils and 30 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) 12 (d) 6
34. 34.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) 90 min (d) 33 min
35. 35.A teacher has 20 pencils and 70 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 10 (b) 50 (c) 5 (d) 20
36. 36.Two ribbons are 21 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) 21 cm (b) 3 cm (c) 1 cm (d) 168 cm
37. 37.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) 320 min (b) 4 min (c) 36 min (d) 80 min
38. 38.Two bells ring every 20 minutes and every 35 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 700 min (b) 140 min (c) 55 min (d) 5 min
39. 39.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) 50 cm (b) 20 cm (c) 10 cm (d) 5 cm
40. 40.What is the smallest number of sweets that can be shared equally among 6 children or among 15 children, with none left over? (a) 21 (b) 60 (c) 90 (d) 30

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