HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 814 · 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 96 pencils and 108 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 864 (c) 96 (d) 12
2. 2.A teacher has 9 pencils and 21 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 9 (c) 12 (d) 3
3. 3.A teacher has 36 pencils and 63 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 27 (b) 9 (c) 3 (d) 36
4. 4.Two ribbons are 40 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) 32 cm (b) 40 cm (c) 8 cm (d) 4 cm
5. 5.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) 36 (d) 216
6. 6.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) 48 (c) 96 (d) 28
7. 7.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) 1 cm (b) 6 cm (c) 4 cm (d) 2 cm
8. 8.A teacher has 56 pencils and 63 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 504 (c) 7 (d) 56
9. 9.What is the smallest number of sweets that can be shared equally among 8 children or among 12 children, with none left over? (a) 96 (b) 24 (c) 48 (d) 20
10. 10.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) 50 (b) 5 (c) 20 (d) 10
11. 11.Two ribbons are 48 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) 48 cm (b) 6 cm (c) 60 cm (d) 12 cm
12. 12.Two bells ring every 12 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 84 min (b) 3 min (c) 252 min (d) 33 min
13. 13.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) 56 min (b) 22 min (c) 2 min (d) 112 min
14. 14.Two ribbons are 21 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) 84 cm (b) 7 cm (c) 1 cm (d) 21 cm
15. 15.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) 2 (b) 8 (c) 6 (d) 1
16. 16.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
17. 17.A teacher has 16 pencils and 72 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 8 (b) 4 (c) 16 (d) 56
18. 18.Two ribbons are 32 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) 32 cm (b) 288 cm (c) 2 cm (d) 4 cm
19. 19.A teacher has 50 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) 50 (c) 10 (d) 30
20. 20.Two ribbons are 6 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) 4 cm (b) 1 cm (c) 2 cm (d) 6 cm
21. 21.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) 336 min (c) 40 min (d) 84 min
22. 22.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) 12 min (c) 24 min (d) 10 min
23. 23.What is the smallest number of sweets that can be shared equally among 10 children or among 12 children, with none left over? (a) 61 (b) 22 (c) 60 (d) 120
24. 24.Two ribbons are 35 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) 5 cm (b) 1 cm (c) 10 cm (d) 35 cm
25. 25.Two ribbons are 21 cm and 49 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) 28 cm (c) 1 cm (d) 7 cm
26. 26.A teacher has 10 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) 2 (c) 4 (d) 10
27. 27.What is the smallest number of sweets that can be shared equally among 10 children or among 25 children, with none left over? (a) 250 (b) 35 (c) 100 (d) 50
28. 28.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) 2 min (d) 24 min
29. 29.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) 28 (c) 140 (d) 7
30. 30.Two ribbons are 18 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) 3 cm (b) 54 cm (c) 9 cm (d) 18 cm
31. 31.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) 30 cm (b) 3 cm (c) 6 cm (d) 12 cm
32. 32.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) 11 (c) 1 (d) 22
33. 33.A teacher has 35 pencils and 45 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) 35 (d) 1
34. 34.Two bells ring every 12 minutes and every 16 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 48 min (b) 192 min (c) 4 min (d) 28 min
35. 35.What is the smallest number of sweets that can be shared equally among 20 children or among 28 children, with none left over? (a) 48 (b) 560 (c) 280 (d) 140
36. 36.What is the smallest number of sweets that can be shared equally among 9 children or among 15 children, with none left over? (a) 90 (b) 24 (c) 45 (d) 135
37. 37.Two bells ring every 15 minutes and every 35 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 105 min (b) 50 min (c) 525 min (d) 5 min
38. 38.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) 3 min (b) 315 min (c) 36 min (d) 105 min
39. 39.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) 36 (d) 54
40. 40.Two bells ring every 12 minutes and every 15 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 180 min (b) 60 min (c) 3 min (d) 27 min

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