HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 342 · 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 10 pencils and 45 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 35 (b) 1 (c) 10 (d) 5
2. 2.What is the smallest number of sweets that can be shared equally among 6 children or among 21 children, with none left over? (a) 84 (b) 27 (c) 42 (d) 126
3. 3.Two ribbons are 35 cm and 49 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) 14 cm (c) 35 cm (d) 1 cm
4. 4.Two bells ring every 9 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 63 min (b) 189 min (c) 3 min (d) 30 min
5. 5.Two bells ring every 12 minutes and every 30 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 6 min (b) 42 min (c) 60 min (d) 360 min
6. 6.A teacher has 10 pencils and 16 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 2 (c) 10 (d) 1
7. 7.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) 300 (c) 60 (d) 120
8. 8.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
9. 9.What is the smallest number of sweets that can be shared equally among 25 children or among 30 children, with none left over? (a) 150 (b) 55 (c) 750 (d) 300
10. 10.A teacher has 20 pencils and 28 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 8 (b) 4 (c) 20 (d) 2
11. 11.What is the smallest number of sweets that can be shared equally among 8 children or among 28 children, with none left over? (a) 224 (b) 36 (c) 112 (d) 56
12. 12.Two ribbons are 33 cm and 77 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) 11 cm (c) 44 cm (d) 33 cm
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) 6 min (b) 504 min (c) 84 min (d) 54 min
14. 14.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
15. 15.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) 28 cm (b) 1 cm (c) 35 cm (d) 7 cm
16. 16.Two ribbons are 20 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) 5 cm (b) 20 cm (c) 10 cm (d) 60 cm
17. 17.A teacher has 14 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) 42 (c) 14 (d) 7
18. 18.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
19. 19.Two ribbons are 96 cm and 108 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 96 cm (b) 864 cm (c) 6 cm (d) 12 cm
20. 20.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) 33 cm (b) 1 cm (c) 11 cm (d) 55 cm
21. 21.What is the smallest number of sweets that can be shared equally among 8 children or among 10 children, with none left over? (a) 41 (b) 80 (c) 18 (d) 40
22. 22.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) 40 min (b) 28 min (c) 4 min (d) 160 min
23. 23.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) 700 min (d) 140 min
24. 24.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) 250 min (c) 5 min (d) 50 min
25. 25.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) 10 (b) 50 (c) 300 (d) 5
26. 26.What is the smallest number of sweets that can be shared equally among 4 children or among 6 children, with none left over? (a) 12 (b) 10 (c) 13 (d) 24
27. 27.A teacher has 40 pencils and 72 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 40 (b) 8 (c) 32 (d) 4
28. 28.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) 432 min (b) 42 min (c) 72 min (d) 6 min
29. 29.Two bells ring every 15 minutes and every 20 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 300 min (b) 35 min (c) 5 min (d) 60 min
30. 30.Two ribbons are 28 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) 35 cm (b) 1 cm (c) 28 cm (d) 7 cm
31. 31.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) 108 min (c) 21 min (d) 36 min
32. 32.Two ribbons are 10 cm and 16 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) 2 cm (c) 1 cm (d) 6 cm
33. 33.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) 90 min (b) 540 min (c) 48 min (d) 6 min
34. 34.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) 5 min (b) 45 min (c) 350 min (d) 70 min
35. 35.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) 45 min (b) 3 min (c) 135 min (d) 24 min
36. 36.A teacher has 24 pencils and 32 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 4 (b) 96 (c) 24 (d) 8
37. 37.Two bells ring every 20 minutes and every 28 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 560 min (b) 48 min (c) 4 min (d) 140 min
38. 38.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) 21 (b) 1 (c) 6 (d) 3
39. 39.What is the smallest number of sweets that can be shared equally among 6 children or among 9 children, with none left over? (a) 54 (b) 36 (c) 18 (d) 15
40. 40.A teacher has 84 pencils and 96 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 672 (b) 6 (c) 84 (d) 12

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