HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 420 · 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 9 children or among 15 children, with none left over? (a) 45 (b) 135 (c) 90 (d) 24
2. 2.Two ribbons are 12 cm and 42 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) 30 cm (d) 6 cm
3. 3.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) 250 min (b) 35 min (c) 50 min (d) 5 min
4. 4.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) 44 min (b) 4 min (c) 120 min (d) 480 min
5. 5.Two ribbons are 24 cm and 60 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) 36 cm (c) 6 cm (d) 12 cm
6. 6.A teacher has 40 pencils and 70 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 5 (b) 40 (c) 30 (d) 10
7. 7.Two ribbons are 25 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) 1 cm (b) 150 cm (c) 5 cm (d) 25 cm
8. 8.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
9. 9.A teacher has 36 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) 36 (c) 60 (d) 12
10. 10.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) 150 min (b) 5 min (c) 25 min (d) 30 min
11. 11.A teacher has 72 pencils and 84 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 12 (c) 504 (d) 72
12. 12.A teacher has 36 pencils and 45 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 180 (b) 9 (c) 3 (d) 36
13. 13.Two ribbons are 96 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) 96 cm (b) 864 cm (c) 12 cm (d) 6 cm
14. 14.What is the smallest number of sweets that can be shared equally among 12 children or among 30 children, with none left over? (a) 120 (b) 60 (c) 42 (d) 360
15. 15.Two ribbons are 4 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) 2 cm (b) 1 cm (c) 4 cm (d) 6 cm
16. 16.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) 22 (c) 1 (d) 11
17. 17.A teacher has 16 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) 16 (c) 4 (d) 8
18. 18.A teacher has 45 pencils and 81 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) 45 (d) 36
19. 19.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) 32 (c) 120 (d) 60
20. 20.Two bells ring every 10 minutes and every 12 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 60 min (b) 22 min (c) 2 min (d) 120 min
21. 21.A teacher has 24 pencils and 27 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 24 (b) 216 (c) 1 (d) 3
22. 22.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) 6 min (c) 120 min (d) 720 min
23. 23.A teacher has 77 pencils and 99 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 77 (c) 11 (d) 22
24. 24.A teacher has 6 pencils and 14 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 8 (b) 6 (c) 2 (d) 1
25. 25.Two ribbons are 24 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) 24 cm (b) 12 cm (c) 84 cm (d) 6 cm
26. 26.Two bells ring every 20 minutes and every 28 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 4 min (b) 48 min (c) 140 min (d) 560 min
27. 27.A teacher has 48 pencils and 108 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) 60 (d) 48
28. 28.A teacher has 21 pencils and 27 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 21 (c) 3 (d) 1
29. 29.Two ribbons are 8 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) 2 cm (b) 1 cm (c) 40 cm (d) 8 cm
30. 30.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) 1 (c) 3 (d) 15
31. 31.Two bells ring every 15 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 36 min (b) 105 min (c) 3 min (d) 315 min
32. 32.What is the smallest number of sweets that can be shared equally among 15 children or among 35 children, with none left over? (a) 210 (b) 105 (c) 525 (d) 50
33. 33.Two ribbons are 24 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) 24 cm (b) 168 cm (c) 4 cm (d) 2 cm
34. 34.What is the smallest number of sweets that can be shared equally among 4 children or among 10 children, with none left over? (a) 20 (b) 40 (c) 21 (d) 14
35. 35.What is the smallest number of sweets that can be shared equally among 6 children or among 9 children, with none left over? (a) 18 (b) 15 (c) 54 (d) 36
36. 36.What is the smallest number of sweets that can be shared equally among 12 children or among 16 children, with none left over? (a) 192 (b) 28 (c) 48 (d) 96
37. 37.Two ribbons are 32 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) 8 cm (b) 4 cm (c) 32 cm (d) 160 cm
38. 38.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) 3 (b) 63 (c) 504 (d) 9
39. 39.Two ribbons are 25 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
40. 40.What is the smallest number of sweets that can be shared equally among 8 children or among 20 children, with none left over? (a) 28 (b) 80 (c) 40 (d) 160

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