HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 325 · 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 72 pencils and 81 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 9 (b) 648 (c) 72 (d) 3
2. 2.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) 2 cm (c) 6 cm (d) 4 cm
3. 3.A teacher has 18 pencils and 48 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 18 (c) 3 (d) 30
4. 4.Two ribbons are 42 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) 1 cm (b) 7 cm (c) 294 cm (d) 42 cm
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) 700 min (b) 5 min (c) 55 min (d) 140 min
6. 6.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
7. 7.A teacher has 22 pencils and 99 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 77 (b) 22 (c) 1 (d) 11
8. 8.Two bells ring every 15 minutes and every 20 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 300 min (b) 60 min (c) 35 min (d) 5 min
9. 9.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) 28 min (b) 4 min (c) 160 min (d) 40 min
10. 10.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) 20 min (b) 14 min (c) 40 min (d) 2 min
11. 11.A teacher has 4 pencils and 6 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 12 (b) 2 (c) 1 (d) 4
12. 12.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) 1 cm (b) 35 cm (c) 10 cm (d) 5 cm
13. 13.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) 10 cm (b) 35 cm (c) 5 cm (d) 1 cm
14. 14.Two bells ring every 25 minutes and every 30 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 150 min (b) 750 min (c) 5 min (d) 55 min
15. 15.Two ribbons are 28 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
16. 16.Two ribbons are 63 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) 9 cm (b) 63 cm (c) 504 cm (d) 3 cm
17. 17.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) 1 (c) 55 (d) 11
18. 18.What is the smallest number of sweets that can be shared equally among 6 children or among 8 children, with none left over? (a) 48 (b) 25 (c) 14 (d) 24
19. 19.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) 21 cm (b) 1 cm (c) 84 cm (d) 7 cm
20. 20.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) 5 min (b) 50 min (c) 525 min (d) 105 min
21. 21.A teacher has 49 pencils and 63 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 7 (b) 14 (c) 1 (d) 49
22. 22.Two ribbons are 6 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) 3 cm (c) 21 cm (d) 6 cm
23. 23.What is the smallest number of sweets that can be shared equally among 18 children or among 30 children, with none left over? (a) 180 (b) 90 (c) 540 (d) 48
24. 24.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) 375 (c) 40 (d) 150
25. 25.Two ribbons are 60 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) 6 cm (b) 12 cm (c) 48 cm (d) 60 cm
26. 26.Two bells ring every 20 minutes and every 25 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 45 min (b) 500 min (c) 5 min (d) 100 min
27. 27.A teacher has 20 pencils and 30 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 10 (b) 60 (c) 20 (d) 5
28. 28.What is the smallest number of sweets that can be shared equally among 4 children or among 6 children, with none left over? (a) 13 (b) 24 (c) 10 (d) 12
29. 29.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) 112 min (d) 2 min
30. 30.What is the smallest number of sweets that can be shared equally among 12 children or among 15 children, with none left over? (a) 60 (b) 27 (c) 120 (d) 180
31. 31.Two ribbons are 33 cm and 88 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) 55 cm (c) 11 cm (d) 33 cm
32. 32.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) 60 min (b) 3 min (c) 27 min (d) 180 min
33. 33.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) 1 cm (b) 6 cm (c) 2 cm (d) 8 cm
34. 34.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) 21 (c) 108 (d) 36
35. 35.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) 2 (b) 28 (c) 4 (d) 8
36. 36.Two ribbons are 35 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) 7 cm (b) 14 cm (c) 35 cm (d) 1 cm
37. 37.Two bells ring every 9 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 63 min (b) 189 min (c) 30 min (d) 3 min
38. 38.A teacher has 20 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) 5 (c) 20 (d) 15
39. 39.A teacher has 10 pencils and 45 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 35 (b) 5 (c) 1 (d) 10
40. 40.What is the smallest number of sweets that can be shared equally among 4 children or among 10 children, with none left over? (a) 40 (b) 20 (c) 14 (d) 21

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