HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 161 · 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 21 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 9 (c) 3 (d) 12
2. 2.Two ribbons are 72 cm and 81 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) 648 cm (c) 3 cm (d) 72 cm
3. 3.Two bells ring every 12 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 84 min (b) 3 min (c) 33 min (d) 252 min
4. 4.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) 35 min (b) 5 min (c) 50 min (d) 250 min
5. 5.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) 7 cm (c) 14 cm (d) 1 cm
6. 6.Two ribbons are 6 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) 6 cm (c) 2 cm (d) 4 cm
7. 7.What is the smallest number of sweets that can be shared equally among 6 children or among 14 children, with none left over? (a) 20 (b) 84 (c) 42 (d) 43
8. 8.Two ribbons are 77 cm and 99 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 77 cm (b) 11 cm (c) 22 cm (d) 1 cm
9. 9.Two ribbons are 18 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) 1 cm (b) 126 cm (c) 3 cm (d) 18 cm
10. 10.Two bells ring every 8 minutes and every 10 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 2 min (b) 40 min (c) 80 min (d) 18 min
11. 11.Two ribbons are 32 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) 288 cm (c) 32 cm (d) 4 cm
12. 12.What is the smallest number of sweets that can be shared equally among 8 children or among 20 children, with none left over? (a) 28 (b) 80 (c) 40 (d) 160
13. 13.Two ribbons are 10 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) 10 cm (c) 2 cm (d) 4 cm
14. 14.Two ribbons are 16 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) 4 cm (b) 8 cm (c) 24 cm (d) 16 cm
15. 15.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) 10 cm (b) 35 cm (c) 1 cm (d) 5 cm
16. 16.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) 54 min (b) 6 min (c) 84 min (d) 504 min
17. 17.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) 4 min (b) 160 min (c) 28 min (d) 40 min
18. 18.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
19. 19.Two ribbons are 20 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) 2 cm (b) 20 cm (c) 120 cm (d) 4 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) 105 min (c) 525 min (d) 50 min
21. 21.Two bells ring every 24 minutes and every 30 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 54 min (b) 120 min (c) 6 min (d) 720 min
22. 22.What is the smallest number of sweets that can be shared equally among 12 children or among 42 children, with none left over? (a) 54 (b) 168 (c) 504 (d) 84
23. 23.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) 36 min (b) 320 min (c) 80 min (d) 4 min
24. 24.A teacher has 35 pencils and 42 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 7 (c) 35 (d) 210
25. 25.What is the smallest number of sweets that can be shared equally among 4 children or among 10 children, with none left over? (a) 14 (b) 20 (c) 21 (d) 40
26. 26.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) 3 min (b) 21 min (c) 108 min (d) 36 min
27. 27.Two ribbons are 27 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) 3 cm (b) 18 cm (c) 27 cm (d) 9 cm
28. 28.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) 48 min (b) 14 min (c) 2 min (d) 24 min
29. 29.A teacher has 8 pencils and 10 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 2 (b) 40 (c) 8 (d) 1
30. 30.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) 180 min (c) 27 min (d) 3 min
31. 31.A teacher has 40 pencils and 90 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 5 (b) 10 (c) 50 (d) 40
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) 15 min (b) 3 min (c) 54 min (d) 18 min
33. 33.What is the smallest number of sweets that can be shared equally among 4 children or among 14 children, with none left over? (a) 56 (b) 29 (c) 28 (d) 18
34. 34.Two ribbons are 40 cm and 48 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) 240 cm (c) 8 cm (d) 4 cm
35. 35.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) 3 (b) 9 (c) 18 (d) 27
36. 36.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) 36 (b) 9 (c) 3 (d) 1
37. 37.Two ribbons are 36 cm and 81 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) 3 cm (c) 45 cm (d) 9 cm
38. 38.Two ribbons are 36 cm and 42 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) 36 cm (c) 3 cm (d) 252 cm
39. 39.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) 36 min (b) 3 min (c) 105 min (d) 315 min
40. 40.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) 20 min (d) 24 min

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