HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 503 · 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 30 pencils and 40 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 10 (b) 120 (c) 5 (d) 30
2. 2.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) 36 (b) 3 (c) 9 (d) 27
3. 3.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
4. 4.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) 70 (b) 5 (c) 20 (d) 10
5. 5.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) 16 cm (c) 2 cm (d) 4 cm
6. 6.Two ribbons are 12 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) 12 cm (b) 16 cm (c) 2 cm (d) 4 cm
7. 7.Two ribbons are 4 cm and 6 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) 2 cm (c) 1 cm (d) 12 cm
8. 8.What is the smallest number of sweets that can be shared equally among 6 children or among 15 children, with none left over? (a) 90 (b) 60 (c) 30 (d) 21
9. 9.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) 1 (b) 36 (c) 9 (d) 3
10. 10.Two bells ring every 8 minutes and every 28 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 56 min (b) 4 min (c) 36 min (d) 224 min
11. 11.Two bells ring every 15 minutes and every 18 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 3 min (b) 270 min (c) 33 min (d) 90 min
12. 12.Two bells ring every 10 minutes and every 25 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 5 min (b) 250 min (c) 35 min (d) 50 min
13. 13.A teacher has 36 pencils and 42 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 252 (c) 6 (d) 36
14. 14.Two ribbons are 21 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) 7 cm (c) 21 cm (d) 14 cm
15. 15.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) 18 cm (b) 12 cm (c) 3 cm (d) 6 cm
16. 16.Two ribbons are 40 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) 40 cm (b) 10 cm (c) 50 cm (d) 5 cm
17. 17.What is the smallest number of sweets that can be shared equally among 9 children or among 21 children, with none left over? (a) 126 (b) 189 (c) 63 (d) 30
18. 18.A teacher has 50 pencils and 60 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 300 (b) 50 (c) 10 (d) 5
19. 19.Two ribbons are 25 cm and 40 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) 15 cm
20. 20.Two ribbons are 10 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) 5 cm (c) 10 cm (d) 25 cm
21. 21.Two bells ring every 16 minutes and every 28 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 112 min (b) 4 min (c) 448 min (d) 44 min
22. 22.A teacher has 54 pencils and 63 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 54 (b) 3 (c) 9 (d) 378
23. 23.What is the smallest number of sweets that can be shared equally among 12 children or among 14 children, with none left over? (a) 26 (b) 85 (c) 84 (d) 168
24. 24.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
25. 25.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) 40 cm (b) 8 cm (c) 4 cm (d) 32 cm
26. 26.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) 375 min (b) 75 min (c) 40 min (d) 5 min
27. 27.Two ribbons are 33 cm and 55 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) 33 cm
28. 28.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) 504 min (b) 84 min (c) 6 min (d) 54 min
29. 29.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) 27 min (b) 180 min (c) 60 min (d) 3 min
30. 30.Two bells ring every 6 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 27 min (b) 3 min (c) 126 min (d) 42 min
31. 31.What is the smallest number of sweets that can be shared equally among 20 children or among 28 children, with none left over? (a) 140 (b) 48 (c) 560 (d) 280
32. 32.Two ribbons are 55 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) 55 cm (b) 33 cm (c) 1 cm (d) 11 cm
33. 33.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
34. 34.Two ribbons are 27 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) 36 cm (c) 3 cm (d) 27 cm
35. 35.Two bells ring every 18 minutes and every 24 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 42 min (b) 432 min (c) 6 min (d) 72 min
36. 36.Two ribbons are 49 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) 49 cm (b) 1 cm (c) 7 cm (d) 14 cm
37. 37.A teacher has 6 pencils and 27 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 3 (c) 6 (d) 21
38. 38.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) 10 min (b) 24 min (c) 12 min (d) 2 min
39. 39.Two bells ring every 9 minutes and every 12 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 21 min (b) 108 min (c) 36 min (d) 3 min
40. 40.What is the smallest number of sweets that can be shared equally among 9 children or among 12 children, with none left over? (a) 21 (b) 72 (c) 108 (d) 36

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