HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 996 · 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 10 pencils and 16 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 2 (c) 1 (d) 10
2. 2.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) 1 (b) 33 (c) 22 (d) 11
3. 3.A teacher has 24 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) 24 (d) 8
4. 4.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) 140 (b) 7 (c) 28 (d) 1
5. 5.What is the smallest number of sweets that can be shared equally among 12 children or among 30 children, with none left over? (a) 60 (b) 42 (c) 360 (d) 120
6. 6.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) 30 (c) 216 (d) 36
7. 7.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) 160 cm (c) 4 cm (d) 32 cm
8. 8.What is the smallest number of sweets that can be shared equally among 9 children or among 15 children, with none left over? (a) 135 (b) 24 (c) 45 (d) 90
9. 9.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) 35 min (b) 250 min (c) 50 min (d) 5 min
10. 10.What is the smallest number of sweets that can be shared equally among 16 children or among 28 children, with none left over? (a) 112 (b) 448 (c) 44 (d) 224
11. 11.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) 12 (b) 24 (c) 36 (d) 6
12. 12.Two bells ring every 12 minutes and every 42 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 84 min (b) 504 min (c) 6 min (d) 54 min
13. 13.Two bells ring every 6 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 84 min (b) 20 min (c) 42 min (d) 2 min
14. 14.Two ribbons are 20 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) 10 cm (b) 70 cm (c) 20 cm (d) 5 cm
15. 15.Two bells ring every 12 minutes and every 20 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 60 min (b) 32 min (c) 240 min (d) 4 min
16. 16.What is the smallest number of sweets that can be shared equally among 15 children or among 21 children, with none left over? (a) 315 (b) 36 (c) 105 (d) 210
17. 17.Two ribbons are 40 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) 5 cm (b) 40 cm (c) 10 cm (d) 50 cm
18. 18.Two ribbons are 36 cm and 84 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 48 cm (b) 36 cm (c) 6 cm (d) 12 cm
19. 19.A teacher has 16 pencils and 28 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 12 (b) 16 (c) 2 (d) 4
20. 20.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) 720 min (b) 6 min (c) 120 min (d) 54 min
21. 21.What is the smallest number of sweets that can be shared equally among 10 children or among 12 children, with none left over? (a) 22 (b) 61 (c) 60 (d) 120
22. 22.Two ribbons are 48 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) 432 cm (b) 48 cm (c) 3 cm (d) 6 cm
23. 23.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) 224 min (b) 56 min (c) 4 min (d) 36 min
24. 24.Two ribbons are 55 cm and 66 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) 330 cm (c) 11 cm (d) 55 cm
25. 25.What is the smallest number of sweets that can be shared equally among 8 children or among 10 children, with none left over? (a) 41 (b) 80 (c) 40 (d) 18
26. 26.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) 1 (b) 24 (c) 3 (d) 216
27. 27.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) 20 (c) 42 (d) 84
28. 28.What is the smallest number of sweets that can be shared equally among 24 children or among 30 children, with none left over? (a) 720 (b) 120 (c) 240 (d) 54
29. 29.A teacher has 18 pencils and 24 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 6 (c) 72 (d) 18
30. 30.A teacher has 25 pencils and 45 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) 25 (d) 1
31. 31.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) 168 cm (b) 2 cm (c) 4 cm (d) 24 cm
32. 32.A teacher has 40 pencils and 50 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) 10 (d) 200
33. 33.Two bells ring every 12 minutes and every 30 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 360 min (b) 60 min (c) 42 min (d) 6 min
34. 34.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) 7 cm (b) 21 cm (c) 35 cm (d) 1 cm
35. 35.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) 36 min (c) 108 min (d) 21 min
36. 36.Two ribbons are 20 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) 20 cm (b) 8 cm (c) 4 cm (d) 2 cm
37. 37.Two bells ring every 18 minutes and every 30 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 48 min (b) 540 min (c) 6 min (d) 90 min
38. 38.A teacher has 10 pencils and 35 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 10 (b) 25 (c) 1 (d) 5
39. 39.A teacher has 15 pencils and 20 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 15 (b) 1 (c) 60 (d) 5
40. 40.What is the smallest number of sweets that can be shared equally among 18 children or among 42 children, with none left over? (a) 126 (b) 60 (c) 252 (d) 756

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