HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 800 · 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 9 minutes and every 15 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 135 min (b) 3 min (c) 45 min (d) 24 min
2. 2.A teacher has 50 pencils and 90 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 50 (b) 40 (c) 5 (d) 10
3. 3.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) 8 cm (b) 2 cm (c) 28 cm (d) 4 cm
4. 4.Two ribbons are 27 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) 3 cm (c) 45 cm (d) 27 cm
5. 5.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) 180 (c) 90 (d) 33
6. 6.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) 4 (b) 160 (c) 32 (d) 8
7. 7.Two bells ring every 12 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 26 min (b) 168 min (c) 2 min (d) 84 min
8. 8.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) 36 min (c) 6 min (d) 30 min
9. 9.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) 32 cm (c) 288 cm (d) 4 cm
10. 10.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
11. 11.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) 20 cm (b) 2 cm (c) 4 cm (d) 8 cm
12. 12.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) 252 min (b) 33 min (c) 84 min (d) 3 min
13. 13.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
14. 14.A teacher has 36 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) 36 (c) 12 (d) 48
15. 15.A teacher has 24 pencils and 108 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 84 (c) 12 (d) 24
16. 16.What is the smallest number of sweets that can be shared equally among 16 children or among 28 children, with none left over? (a) 44 (b) 224 (c) 112 (d) 448
17. 17.Two ribbons are 49 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) 392 cm (b) 7 cm (c) 49 cm (d) 1 cm
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) 14 (b) 25 (c) 24 (d) 48
19. 19.Two bells ring every 4 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 56 min (b) 18 min (c) 2 min (d) 28 min
20. 20.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
21. 21.What is the smallest number of sweets that can be shared equally among 6 children or among 9 children, with none left over? (a) 18 (b) 36 (c) 54 (d) 15
22. 22.A teacher has 21 pencils and 56 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 35 (c) 21 (d) 7
23. 23.Two bells ring every 18 minutes and every 42 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 60 min (b) 126 min (c) 6 min (d) 756 min
24. 24.A teacher has 12 pencils and 54 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 42 (c) 12 (d) 3
25. 25.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
26. 26.A teacher has 24 pencils and 54 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 24 (b) 30 (c) 6 (d) 3
27. 27.A teacher has 32 pencils and 36 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 32 (b) 2 (c) 4 (d) 288
28. 28.A teacher has 12 pencils and 28 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 2 (b) 16 (c) 12 (d) 4
29. 29.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) 8 cm (c) 1 cm (d) 2 cm
30. 30.What is the smallest number of sweets that can be shared equally among 15 children or among 21 children, with none left over? (a) 210 (b) 315 (c) 105 (d) 36
31. 31.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) 5 min (b) 750 min (c) 55 min (d) 150 min
32. 32.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) 2 (b) 4 (c) 16 (d) 20
33. 33.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) 2 (b) 1 (c) 10 (d) 6
34. 34.Two ribbons are 9 cm and 15 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) 1 cm (c) 6 cm (d) 9 cm
35. 35.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) 720 min (b) 6 min (c) 54 min (d) 120 min
36. 36.A teacher has 30 pencils and 42 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 12 (b) 30 (c) 6 (d) 3
37. 37.Two ribbons are 6 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) 15 cm (b) 1 cm (c) 6 cm (d) 3 cm
38. 38.A teacher has 18 pencils and 30 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 18 (b) 3 (c) 12 (d) 6
39. 39.What is the smallest number of sweets that can be shared equally among 18 children or among 21 children, with none left over? (a) 252 (b) 39 (c) 378 (d) 126
40. 40.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) 54 min (c) 3 min (d) 18 min

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