HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 443 · 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 30 children, with none left over? (a) 120 (b) 42 (c) 60 (d) 360
2. 2.Two ribbons are 10 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) 1 cm (b) 10 cm (c) 8 cm (d) 2 cm
3. 3.Two bells ring every 16 minutes and every 28 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 448 min (b) 4 min (c) 112 min (d) 44 min
4. 4.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) 5 (b) 10 (c) 20 (d) 50
5. 5.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) 72 cm (b) 18 cm (c) 6 cm (d) 3 cm
6. 6.A teacher has 12 pencils and 42 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 12 (c) 30 (d) 6
7. 7.Two ribbons are 30 cm and 36 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 30 cm (b) 6 cm (c) 180 cm (d) 3 cm
8. 8.What is the smallest number of sweets that can be shared equally among 6 children or among 14 children, with none left over? (a) 43 (b) 84 (c) 20 (d) 42
9. 9.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) 24 (b) 6 (c) 12 (d) 36
10. 10.Two bells ring every 4 minutes and every 10 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 40 min (b) 20 min (c) 14 min (d) 2 min
11. 11.Two ribbons are 15 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) 1 cm (b) 15 cm (c) 25 cm (d) 5 cm
12. 12.Two bells ring every 9 minutes and every 15 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 24 min (b) 45 min (c) 3 min (d) 135 min
13. 13.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) 4 min (b) 40 min (c) 84 min (d) 336 min
14. 14.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) 48 min (b) 24 min (c) 2 min (d) 14 min
15. 15.What is the smallest number of sweets that can be shared equally among 8 children or among 12 children, with none left over? (a) 48 (b) 24 (c) 20 (d) 96
16. 16.Two ribbons are 25 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) 1 cm (b) 25 cm (c) 5 cm (d) 15 cm
17. 17.Two ribbons are 15 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) 15 cm (b) 3 cm (c) 1 cm (d) 90 cm
18. 18.A teacher has 27 pencils and 63 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 36 (b) 9 (c) 3 (d) 27
19. 19.Two bells ring every 10 minutes and every 35 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 350 min (b) 5 min (c) 45 min (d) 70 min
20. 20.Two ribbons are 88 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) 11 cm (b) 1 cm (c) 792 cm (d) 88 cm
21. 21.What is the smallest number of sweets that can be shared equally among 12 children or among 20 children, with none left over? (a) 32 (b) 120 (c) 240 (d) 60
22. 22.A teacher has 15 pencils and 40 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) 25 (d) 15
23. 23.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) 60 min (b) 35 min (c) 300 min (d) 5 min
24. 24.What is the smallest number of sweets that can be shared equally among 16 children or among 20 children, with none left over? (a) 80 (b) 36 (c) 320 (d) 160
25. 25.A teacher has 80 pencils and 90 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 5 (b) 80 (c) 720 (d) 10
26. 26.Two ribbons are 15 cm and 20 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) 15 cm (c) 5 cm (d) 60 cm
27. 27.Two ribbons are 24 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) 3 cm (b) 24 cm (c) 6 cm (d) 30 cm
28. 28.A teacher has 42 pencils and 49 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 294 (b) 7 (c) 42 (d) 1
29. 29.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) 56 min (b) 18 min (c) 2 min (d) 28 min
30. 30.A teacher has 9 pencils and 12 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 9 (b) 36 (c) 1 (d) 3
31. 31.A teacher has 36 pencils and 42 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) 252
32. 32.A teacher has 18 pencils and 45 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 9 (c) 27 (d) 18
33. 33.A teacher has 56 pencils and 64 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 4 (b) 56 (c) 8 (d) 448
34. 34.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) 160 min (b) 4 min (c) 28 min (d) 40 min
35. 35.A teacher has 20 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
36. 36.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) 4 cm (b) 8 cm (c) 56 cm (d) 16 cm
37. 37.A teacher has 18 pencils and 48 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 18 (b) 30 (c) 3 (d) 6
38. 38.What is the smallest number of sweets that can be shared equally among 24 children or among 30 children, with none left over? (a) 240 (b) 120 (c) 54 (d) 720
39. 39.A teacher has 63 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) 18 (d) 63
40. 40.What is the smallest number of sweets that can be shared equally among 12 children or among 28 children, with none left over? (a) 168 (b) 336 (c) 40 (d) 84

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