HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 964 · 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 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) 36 min (b) 4 min (c) 56 min (d) 224 min
2. 2.What is the smallest number of sweets that can be shared equally among 6 children or among 10 children, with none left over? (a) 16 (b) 31 (c) 60 (d) 30
3. 3.A teacher has 32 pencils and 40 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 32 (b) 4 (c) 160 (d) 8
4. 4.A teacher has 30 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) 30 (d) 210
5. 5.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) 44 min (c) 4 min (d) 448 min
6. 6.What is the smallest number of sweets that can be shared equally among 20 children or among 24 children, with none left over? (a) 240 (b) 44 (c) 120 (d) 480
7. 7.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) 33 min (b) 252 min (c) 84 min (d) 3 min
8. 8.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) 20 min (c) 84 min (d) 42 min
9. 9.A teacher has 50 pencils and 70 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 50 (b) 20 (c) 5 (d) 10
10. 10.Two bells ring every 10 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 70 min (b) 24 min (c) 2 min (d) 140 min
11. 11.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) 4 cm (b) 12 cm (c) 2 cm (d) 16 cm
12. 12.A teacher has 6 pencils and 16 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 10 (b) 2 (c) 6 (d) 1
13. 13.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) 84 min (b) 54 min (c) 6 min (d) 504 min
14. 14.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
15. 15.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) 5 min (b) 375 min (c) 75 min (d) 40 min
16. 16.What is the smallest number of sweets that can be shared equally among 15 children or among 18 children, with none left over? (a) 270 (b) 33 (c) 180 (d) 90
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) 63 (c) 30 (d) 189
18. 18.Two ribbons are 15 cm and 20 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) 60 cm (d) 5 cm
19. 19.Two ribbons are 28 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) 28 cm (c) 4 cm (d) 8 cm
20. 20.What is the smallest number of sweets that can be shared equally among 15 children or among 25 children, with none left over? (a) 375 (b) 40 (c) 150 (d) 75
21. 21.A teacher has 10 pencils and 12 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 60 (b) 10 (c) 2 (d) 1
22. 22.Two ribbons are 4 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) 14 cm (b) 4 cm (c) 1 cm (d) 2 cm
23. 23.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) 126 min (b) 42 min (c) 27 min (d) 3 min
24. 24.Two ribbons are 16 cm and 56 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) 4 cm (c) 8 cm (d) 16 cm
25. 25.What is the smallest number of sweets that can be shared equally among 10 children or among 25 children, with none left over? (a) 35 (b) 100 (c) 50 (d) 250
26. 26.Two ribbons are 30 cm and 80 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) 30 cm (d) 50 cm
27. 27.A teacher has 30 pencils and 48 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 30 (b) 3 (c) 18 (d) 6
28. 28.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) 54 min (b) 18 min (c) 15 min (d) 3 min
29. 29.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) 336 min (b) 84 min (c) 4 min (d) 40 min
30. 30.Two ribbons are 16 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) 2 cm (c) 16 cm (d) 12 cm
31. 31.Two ribbons are 10 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) 10 cm (b) 1 cm (c) 8 cm (d) 2 cm
32. 32.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) 2 min (b) 30 min (c) 60 min (d) 16 min
33. 33.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) 24 cm (b) 6 cm (c) 2 cm (d) 1 cm
34. 34.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) 84 (c) 40 (d) 168
35. 35.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) 3 cm (b) 252 cm (c) 36 cm (d) 6 cm
36. 36.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) 50 cm (b) 40 cm (c) 10 cm (d) 5 cm
37. 37.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) 24 min (b) 2 min (c) 48 min (d) 14 min
38. 38.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) 500 min (b) 45 min (c) 100 min (d) 5 min
39. 39.A teacher has 9 pencils and 15 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 6 (c) 9 (d) 1
40. 40.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) 55 min (b) 5 min (c) 140 min (d) 700 min

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