HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 605 · 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 14 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) 4 cm (b) 1 cm (c) 14 cm (d) 2 cm
2. 2.Two ribbons are 8 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) 4 cm (b) 20 cm (c) 8 cm (d) 2 cm
3. 3.Two ribbons are 14 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) 21 cm (b) 1 cm (c) 7 cm (d) 14 cm
4. 4.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) 71 (c) 140 (d) 70
5. 5.Two bells ring every 9 minutes and every 15 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 3 min (b) 135 min (c) 45 min (d) 24 min
6. 6.Two ribbons are 15 cm and 24 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 15 cm (b) 1 cm (c) 3 cm (d) 9 cm
7. 7.Two ribbons are 12 cm and 16 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) 48 cm (c) 12 cm (d) 4 cm
8. 8.Two ribbons are 6 cm and 8 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) 24 cm (c) 6 cm (d) 1 cm
9. 9.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) 3 min (c) 30 min (d) 189 min
10. 10.Two ribbons are 10 cm and 25 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 15 cm (b) 5 cm (c) 1 cm (d) 10 cm
11. 11.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) 60 (c) 120 (d) 61
12. 12.Two bells ring every 12 minutes and every 18 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 216 min (b) 6 min (c) 36 min (d) 30 min
13. 13.Two ribbons are 27 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) 9 cm (b) 3 cm (c) 27 cm (d) 108 cm
14. 14.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) 2 (b) 12 (c) 4 (d) 1
15. 15.Two ribbons are 28 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) 1 cm (b) 28 cm (c) 140 cm (d) 7 cm
16. 16.A teacher has 15 pencils and 35 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) 5 (d) 20
17. 17.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) 6 (b) 24 (c) 60 (d) 12
18. 18.Two bells ring every 6 minutes and every 10 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 16 min (b) 2 min (c) 30 min (d) 60 min
19. 19.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
20. 20.What is the smallest number of sweets that can be shared equally among 12 children or among 16 children, with none left over? (a) 96 (b) 28 (c) 48 (d) 192
21. 21.What is the smallest number of sweets that can be shared equally among 12 children or among 14 children, with none left over? (a) 85 (b) 84 (c) 168 (d) 26
22. 22.What is the smallest number of sweets that can be shared equally among 6 children or among 21 children, with none left over? (a) 126 (b) 27 (c) 42 (d) 84
23. 23.Two bells ring every 10 minutes and every 12 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 22 min (b) 60 min (c) 120 min (d) 2 min
24. 24.What is the smallest number of sweets that can be shared equally among 4 children or among 10 children, with none left over? (a) 20 (b) 21 (c) 14 (d) 40
25. 25.What is the smallest number of sweets that can be shared equally among 12 children or among 21 children, with none left over? (a) 168 (b) 84 (c) 252 (d) 33
26. 26.What is the smallest number of sweets that can be shared equally among 12 children or among 18 children, with none left over? (a) 216 (b) 72 (c) 30 (d) 36
27. 27.A teacher has 12 pencils and 14 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) 84
28. 28.What is the smallest number of sweets that can be shared equally among 12 children or among 15 children, with none left over? (a) 180 (b) 120 (c) 60 (d) 27
29. 29.A teacher has 60 pencils and 72 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 360 (c) 60 (d) 12
30. 30.Two ribbons are 20 cm and 25 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) 1 cm (c) 5 cm (d) 100 cm
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) 33 cm (d) 11 cm
32. 32.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) 20 min (b) 4 min (c) 24 min (d) 96 min
33. 33.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) 55 (b) 33 (c) 11 (d) 1
34. 34.A teacher has 33 pencils and 77 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 11 (c) 33 (d) 44
35. 35.A teacher has 33 pencils and 88 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) 11 (d) 55
36. 36.Two ribbons are 12 cm and 30 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 12 cm (b) 18 cm (c) 3 cm (d) 6 cm
37. 37.Two ribbons are 14 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) 14 cm (b) 7 cm (c) 1 cm (d) 42 cm
38. 38.Two ribbons are 48 cm and 60 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 240 cm (b) 12 cm (c) 48 cm (d) 6 cm
39. 39.A teacher has 27 pencils and 63 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 36 (c) 27 (d) 9
40. 40.What is the smallest number of sweets that can be shared equally among 10 children or among 15 children, with none left over? (a) 150 (b) 30 (c) 25 (d) 60

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