HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 315 · 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 54 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 12 (c) 6 (d) 42
2. 2.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) 10 (d) 5
3. 3.Two ribbons are 20 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) 5 cm (b) 10 cm (c) 70 cm (d) 20 cm
4. 4.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) 2 cm (b) 4 cm (c) 12 cm (d) 16 cm
5. 5.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) 4 min (b) 56 min (c) 36 min (d) 224 min
6. 6.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
7. 7.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) 525 min (b) 5 min (c) 50 min (d) 105 min
8. 8.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) 140 min (d) 55 min
9. 9.Two ribbons are 25 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) 25 cm (c) 5 cm (d) 10 cm
10. 10.A teacher has 40 pencils and 48 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 240 (b) 40 (c) 8 (d) 4
11. 11.A teacher has 4 pencils and 18 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 4 (b) 1 (c) 2 (d) 14
12. 12.What is the smallest number of sweets that can be shared equally among 24 children or among 30 children, with none left over? (a) 120 (b) 240 (c) 54 (d) 720
13. 13.What is the smallest number of sweets that can be shared equally among 8 children or among 10 children, with none left over? (a) 80 (b) 18 (c) 41 (d) 40
14. 14.Two bells ring every 18 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 3 min (b) 378 min (c) 126 min (d) 39 min
15. 15.A teacher has 6 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) 6 (c) 15 (d) 3
16. 16.What is the smallest number of sweets that can be shared equally among 12 children or among 18 children, with none left over? (a) 72 (b) 30 (c) 36 (d) 216
17. 17.Two bells ring every 20 minutes and every 24 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 480 min (b) 4 min (c) 44 min (d) 120 min
18. 18.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) 84 min (b) 168 min (c) 2 min (d) 26 min
19. 19.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) 2 min (b) 24 min (c) 70 min (d) 140 min
20. 20.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) 50 min (c) 250 min (d) 5 min
21. 21.A teacher has 28 pencils and 49 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 21 (c) 7 (d) 28
22. 22.Two bells ring every 4 minutes and every 10 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 14 min (b) 40 min (c) 2 min (d) 20 min
23. 23.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) 6 min (c) 432 min (d) 72 min
24. 24.Two ribbons are 30 cm and 50 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 30 cm (b) 5 cm (c) 10 cm (d) 20 cm
25. 25.A teacher has 36 pencils and 96 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 60 (b) 36 (c) 12 (d) 6
26. 26.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) 750 min (b) 150 min (c) 55 min (d) 5 min
27. 27.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) 270 min (b) 90 min (c) 3 min (d) 33 min
28. 28.What is the smallest number of sweets that can be shared equally among 18 children or among 42 children, with none left over? (a) 252 (b) 756 (c) 60 (d) 126
29. 29.Two bells ring every 18 minutes and every 30 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 48 min (b) 90 min (c) 6 min (d) 540 min
30. 30.Two ribbons are 35 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) 7 cm (b) 28 cm (c) 35 cm (d) 1 cm
31. 31.A teacher has 40 pencils and 70 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 40 (b) 30 (c) 10 (d) 5
32. 32.Two bells ring every 10 minutes and every 35 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 70 min (b) 45 min (c) 350 min (d) 5 min
33. 33.A teacher has 22 pencils and 33 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 11 (b) 66 (c) 22 (d) 1
34. 34.What is the smallest number of sweets that can be shared equally among 15 children or among 20 children, with none left over? (a) 35 (b) 120 (c) 300 (d) 60
35. 35.Two bells ring every 10 minutes and every 15 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 25 min (b) 30 min (c) 150 min (d) 5 min
36. 36.A teacher has 27 pencils and 72 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 9 (b) 27 (c) 3 (d) 45
37. 37.What is the smallest number of sweets that can be shared equally among 6 children or among 10 children, with none left over? (a) 30 (b) 31 (c) 60 (d) 16
38. 38.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) 48 min (c) 24 min (d) 2 min
39. 39.Two ribbons are 6 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) 8 cm (b) 2 cm (c) 1 cm (d) 6 cm
40. 40.What is the smallest number of sweets that can be shared equally among 6 children or among 9 children, with none left over? (a) 36 (b) 54 (c) 15 (d) 18

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