HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 481 · 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 28 pencils and 32 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 224 (b) 4 (c) 28 (d) 2
2. 2.A teacher has 42 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) 3 (c) 42 (d) 6
3. 3.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) 4 cm (b) 40 cm (c) 8 cm (d) 24 cm
4. 4.What is the smallest number of sweets that can be shared equally among 16 children or among 28 children, with none left over? (a) 448 (b) 224 (c) 112 (d) 44
5. 5.Two ribbons are 20 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) 60 cm (b) 10 cm (c) 20 cm (d) 5 cm
6. 6.What is the smallest number of sweets that can be shared equally among 9 children or among 12 children, with none left over? (a) 72 (b) 36 (c) 21 (d) 108
7. 7.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) 56 min (d) 224 min
8. 8.A teacher has 30 pencils and 50 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 20 (b) 5 (c) 10 (d) 30
9. 9.What is the smallest number of sweets that can be shared equally among 12 children or among 42 children, with none left over? (a) 168 (b) 54 (c) 84 (d) 504
10. 10.Two ribbons are 8 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) 2 cm (b) 1 cm (c) 6 cm (d) 8 cm
11. 11.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) 84 min (b) 26 min (c) 2 min (d) 168 min
12. 12.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) 3 min (b) 90 min (c) 21 min (d) 30 min
13. 13.Two bells ring every 4 minutes and every 6 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 2 min (b) 24 min (c) 12 min (d) 10 min
14. 14.What is the smallest number of sweets that can be shared equally among 8 children or among 28 children, with none left over? (a) 224 (b) 36 (c) 56 (d) 112
15. 15.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) 33 min (b) 3 min (c) 90 min (d) 270 min
16. 16.Two ribbons are 54 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) 378 cm (b) 9 cm (c) 3 cm (d) 54 cm
17. 17.What is the smallest number of sweets that can be shared equally among 9 children or among 21 children, with none left over? (a) 30 (b) 126 (c) 189 (d) 63
18. 18.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) 60 (c) 35 (d) 300
19. 19.A teacher has 8 pencils and 14 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) 6 (d) 2
20. 20.Two ribbons are 45 cm and 81 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) 36 cm (d) 45 cm
21. 21.A teacher has 32 pencils and 40 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 4 (b) 32 (c) 8 (d) 160
22. 22.What is the smallest number of sweets that can be shared equally among 6 children or among 9 children, with none left over? (a) 15 (b) 18 (c) 36 (d) 54
23. 23.What is the smallest number of sweets that can be shared equally among 25 children or among 30 children, with none left over? (a) 150 (b) 55 (c) 300 (d) 750
24. 24.Two ribbons are 18 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) 3 cm (b) 27 cm (c) 18 cm (d) 9 cm
25. 25.A teacher has 49 pencils and 56 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 49 (b) 7 (c) 1 (d) 392
26. 26.Two ribbons are 22 cm and 55 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) 22 cm
27. 27.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) 21 cm (b) 7 cm (c) 14 cm (d) 1 cm
28. 28.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) 30 (b) 5 (c) 40 (d) 10
29. 29.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) 60 (c) 90 (d) 21
30. 30.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) 3 min (b) 21 min (c) 108 min (d) 36 min
31. 31.What is the smallest number of sweets that can be shared equally among 10 children or among 35 children, with none left over? (a) 350 (b) 140 (c) 45 (d) 70
32. 32.A teacher has 40 pencils and 72 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 40 (b) 32 (c) 4 (d) 8
33. 33.A teacher has 21 pencils and 24 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 168 (b) 1 (c) 3 (d) 21
34. 34.Two ribbons are 15 cm and 25 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) 5 cm (c) 1 cm (d) 15 cm
35. 35.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) 14 min (b) 40 min (c) 2 min (d) 20 min
36. 36.Two ribbons are 15 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) 15 cm (b) 20 cm (c) 1 cm (d) 5 cm
37. 37.A teacher has 16 pencils and 40 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 4 (b) 16 (c) 8 (d) 24
38. 38.Two bells ring every 10 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 140 min (b) 70 min (c) 24 min (d) 2 min
39. 39.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) 36 (b) 60 (c) 12 (d) 6
40. 40.A teacher has 55 pencils and 66 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 55 (b) 11 (c) 330 (d) 1

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