HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 133 · 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.Two ribbons are 9 cm and 12 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 36 cm (b) 1 cm (c) 3 cm (d) 9 cm
2. 2.A teacher has 15 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) 6 (c) 3 (d) 15
3. 3.What is the smallest number of sweets that can be shared equally among 15 children or among 25 children, with none left over? (a) 75 (b) 40 (c) 150 (d) 375
4. 4.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) 525 min (b) 50 min (c) 5 min (d) 105 min
5. 5.Two bells ring every 20 minutes and every 35 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 5 min (b) 140 min (c) 55 min (d) 700 min
6. 6.Two ribbons are 56 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) 56 cm (c) 16 cm (d) 8 cm
7. 7.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) 45 min (b) 70 min (c) 350 min (d) 5 min
8. 8.A teacher has 55 pencils and 88 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) 55
9. 9.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) 3 cm (b) 36 cm (c) 27 cm (d) 9 cm
10. 10.A teacher has 27 pencils and 45 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 18 (b) 27 (c) 9 (d) 3
11. 11.Two ribbons are 45 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) 18 cm (b) 9 cm (c) 45 cm (d) 3 cm
12. 12.What is the smallest number of sweets that can be shared equally among 15 children or among 18 children, with none left over? (a) 90 (b) 33 (c) 180 (d) 270
13. 13.Two ribbons are 25 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) 10 cm (b) 25 cm (c) 5 cm (d) 1 cm
14. 14.What is the smallest number of sweets that can be shared equally among 9 children or among 15 children, with none left over? (a) 24 (b) 45 (c) 135 (d) 90
15. 15.Two ribbons are 22 cm and 33 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 22 cm (b) 1 cm (c) 11 cm (d) 66 cm
16. 16.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) 24 cm (b) 12 cm (c) 60 cm (d) 6 cm
17. 17.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) 2 min (b) 84 min (c) 20 min (d) 42 min
18. 18.A teacher has 12 pencils and 28 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 2 (b) 4 (c) 12 (d) 16
19. 19.What is the smallest number of sweets that can be shared equally among 18 children or among 24 children, with none left over? (a) 42 (b) 432 (c) 144 (d) 72
20. 20.A teacher has 27 pencils and 36 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 108 (b) 27 (c) 9 (d) 3
21. 21.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) 720 (c) 120 (d) 54
22. 22.What is the smallest number of sweets that can be shared equally among 15 children or among 20 children, with none left over? (a) 300 (b) 35 (c) 60 (d) 120
23. 23.A teacher has 16 pencils and 20 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 4 (b) 80 (c) 2 (d) 16
24. 24.Two ribbons are 10 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) 35 cm (c) 10 cm (d) 1 cm
25. 25.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
26. 26.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) 21 min (c) 90 min (d) 30 min
27. 27.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) 8 (b) 4 (c) 40 (d) 32
28. 28.What is the smallest number of sweets that can be shared equally among 12 children or among 16 children, with none left over? (a) 28 (b) 96 (c) 192 (d) 48
29. 29.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) 2 min (b) 168 min (c) 26 min (d) 84 min
30. 30.A teacher has 20 pencils and 36 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 20 (b) 2 (c) 16 (d) 4
31. 31.Two ribbons are 44 cm and 77 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 33 cm (b) 44 cm (c) 11 cm (d) 1 cm
32. 32.Two bells ring every 6 minutes and every 9 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 3 min (b) 15 min (c) 18 min (d) 54 min
33. 33.Two ribbons are 20 cm and 70 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) 10 cm (c) 50 cm (d) 20 cm
34. 34.A teacher has 24 pencils and 84 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 60 (b) 6 (c) 12 (d) 24
35. 35.Two ribbons are 8 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) 40 cm (c) 8 cm (d) 2 cm
36. 36.A teacher has 27 pencils and 72 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 27 (b) 3 (c) 9 (d) 45
37. 37.A teacher has 70 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) 70 (c) 560 (d) 10
38. 38.What is the smallest number of sweets that can be shared equally among 12 children or among 28 children, with none left over? (a) 336 (b) 168 (c) 84 (d) 40
39. 39.Two ribbons are 6 cm and 21 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) 1 cm (c) 6 cm (d) 15 cm
40. 40.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) 40 min (c) 28 min (d) 4 min

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