HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 72 · 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 12 pencils and 15 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 60 (c) 3 (d) 12
2. 2.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) 10 (b) 200 (c) 5 (d) 40
3. 3.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) 160 (c) 320 (d) 36
4. 4.A teacher has 64 pencils and 72 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 4 (b) 64 (c) 8 (d) 576
5. 5.A teacher has 30 pencils and 54 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 30 (c) 24 (d) 6
6. 6.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) 20 cm (c) 70 cm (d) 5 cm
7. 7.Two bells ring every 8 minutes and every 12 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 4 min (b) 96 min (c) 24 min (d) 20 min
8. 8.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) 14 min (b) 24 min (c) 48 min (d) 2 min
9. 9.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
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) 448 (b) 224 (c) 112 (d) 44
11. 11.What is the smallest number of sweets that can be shared equally among 10 children or among 15 children, with none left over? (a) 30 (b) 60 (c) 25 (d) 150
12. 12.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) 3 (c) 1 (d) 36
13. 13.Two bells ring every 15 minutes and every 25 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 40 min (b) 5 min (c) 375 min (d) 75 min
14. 14.Two ribbons are 8 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
15. 15.Two ribbons are 20 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) 25 cm (d) 20 cm
16. 16.Two ribbons are 8 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) 2 cm (b) 28 cm (c) 8 cm (d) 4 cm
17. 17.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) 105 min (b) 36 min (c) 315 min (d) 3 min
18. 18.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) 6 min (b) 360 min (c) 60 min (d) 42 min
19. 19.Two bells ring every 16 minutes and every 20 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 320 min (b) 4 min (c) 36 min (d) 80 min
20. 20.A teacher has 21 pencils and 35 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 14 (b) 7 (c) 21 (d) 1
21. 21.Two ribbons are 56 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) 504 cm (b) 56 cm (c) 7 cm (d) 1 cm
22. 22.Two ribbons are 16 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) 20 cm (b) 4 cm (c) 2 cm (d) 16 cm
23. 23.A teacher has 14 pencils and 35 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 14 (b) 1 (c) 21 (d) 7
24. 24.A teacher has 24 pencils and 28 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 4 (b) 24 (c) 168 (d) 2
25. 25.Two ribbons are 36 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) 9 cm (b) 3 cm (c) 27 cm (d) 36 cm
26. 26.A teacher has 20 pencils and 90 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 20 (b) 10 (c) 5 (d) 70
27. 27.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) 70 min (c) 5 min (d) 45 min
28. 28.A teacher has 12 pencils and 18 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) 12 (d) 3
29. 29.What is the smallest number of sweets that can be shared equally among 10 children or among 14 children, with none left over? (a) 24 (b) 70 (c) 140 (d) 71
30. 30.Two ribbons are 60 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) 60 cm (b) 6 cm (c) 12 cm (d) 24 cm
31. 31.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
32. 32.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) 10 min (c) 24 min (d) 12 min
33. 33.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) 4 (b) 12 (c) 16 (d) 2
34. 34.What is the smallest number of sweets that can be shared equally among 8 children or among 20 children, with none left over? (a) 40 (b) 80 (c) 28 (d) 160
35. 35.Two ribbons are 12 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) 1 cm (b) 12 cm (c) 3 cm (d) 15 cm
36. 36.A teacher has 12 pencils and 27 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 12 (b) 15 (c) 3 (d) 1
37. 37.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) 28 cm (b) 21 cm (c) 1 cm (d) 7 cm
38. 38.What is the smallest number of sweets that can be shared equally among 4 children or among 6 children, with none left over? (a) 12 (b) 10 (c) 13 (d) 24
39. 39.A teacher has 8 pencils and 36 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 28 (b) 2 (c) 4 (d) 8
40. 40.Two ribbons are 28 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) 1 cm (b) 28 cm (c) 35 cm (d) 7 cm

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