HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 650 · 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 80 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) 80 cm (b) 10 cm (c) 5 cm (d) 720 cm
2. 2.What is the smallest number of sweets that can be shared equally among 4 children or among 10 children, with none left over? (a) 40 (b) 20 (c) 14 (d) 21
3. 3.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) 10 cm (b) 4 cm (c) 1 cm (d) 2 cm
4. 4.A teacher has 40 pencils and 56 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 40 (b) 8 (c) 4 (d) 16
5. 5.Two ribbons are 20 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) 20 cm (b) 2 cm (c) 120 cm (d) 4 cm
6. 6.Two bells ring every 24 minutes and every 30 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 54 min (b) 720 min (c) 120 min (d) 6 min
7. 7.A teacher has 24 pencils and 64 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 24 (b) 40 (c) 4 (d) 8
8. 8.A teacher has 30 pencils and 70 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 40 (b) 30 (c) 10 (d) 5
9. 9.A teacher has 8 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) 10 (c) 2 (d) 8
10. 10.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) 5 min (b) 35 min (c) 50 min (d) 250 min
11. 11.A teacher has 30 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) 30 (c) 5 (d) 10
12. 12.A teacher has 70 pencils and 80 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 5 (b) 560 (c) 10 (d) 70
13. 13.Two bells ring every 6 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 3 min (b) 27 min (c) 42 min (d) 126 min
14. 14.A teacher has 21 pencils and 56 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 21 (b) 1 (c) 7 (d) 35
15. 15.Two ribbons are 12 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) 1 cm (c) 3 cm (d) 15 cm
16. 16.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) 90 min (b) 30 min (c) 3 min (d) 21 min
17. 17.What is the smallest number of sweets that can be shared equally among 9 children or among 15 children, with none left over? (a) 45 (b) 135 (c) 24 (d) 90
18. 18.Two ribbons are 14 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) 14 cm (b) 7 cm (c) 1 cm (d) 21 cm
19. 19.A teacher has 15 pencils and 18 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 15 (b) 3 (c) 90 (d) 1
20. 20.Two ribbons are 35 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) 21 cm (b) 35 cm (c) 7 cm (d) 1 cm
21. 21.A teacher has 15 pencils and 25 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 15 (c) 10 (d) 5
22. 22.A teacher has 28 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) 7 (c) 140 (d) 28
23. 23.Two ribbons are 16 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) 16 cm (b) 4 cm (c) 8 cm (d) 24 cm
24. 24.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) 6 (d) 12
25. 25.A teacher has 35 pencils and 63 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 28 (b) 35 (c) 7 (d) 1
26. 26.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) 27 (c) 180 (d) 120
27. 27.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) 1 cm (b) 77 cm (c) 22 cm (d) 11 cm
28. 28.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) 24 cm (b) 8 cm (c) 40 cm (d) 4 cm
29. 29.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) 224 min (c) 56 min (d) 36 min
30. 30.What is the smallest number of sweets that can be shared equally among 10 children or among 15 children, with none left over? (a) 60 (b) 30 (c) 25 (d) 150
31. 31.A teacher has 6 pencils and 16 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 6 (c) 10 (d) 2
32. 32.Two ribbons are 27 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) 36 cm (b) 3 cm (c) 9 cm (d) 27 cm
33. 33.A teacher has 40 pencils and 48 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 240 (b) 8 (c) 4 (d) 40
34. 34.A teacher has 9 pencils and 24 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 9 (b) 3 (c) 15 (d) 1
35. 35.Two ribbons are 21 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) 1 cm (b) 35 cm (c) 7 cm (d) 21 cm
36. 36.What is the smallest number of sweets that can be shared equally among 6 children or among 8 children, with none left over? (a) 14 (b) 25 (c) 48 (d) 24
37. 37.Two ribbons are 4 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) 2 cm (b) 4 cm (c) 1 cm (d) 14 cm
38. 38.Two ribbons are 30 cm and 48 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) 18 cm (c) 6 cm (d) 30 cm
39. 39.Two ribbons are 12 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) 12 cm (b) 20 cm (c) 4 cm (d) 2 cm
40. 40.Two ribbons are 49 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) 14 cm (b) 1 cm (c) 7 cm (d) 49 cm

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