HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 946 · 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 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) 160 (b) 8 (c) 32 (d) 4
2. 2.Two ribbons are 42 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) 1 cm (b) 294 cm (c) 42 cm (d) 7 cm
3. 3.What is the smallest number of sweets that can be shared equally among 24 children or among 30 children, with none left over? (a) 240 (b) 120 (c) 720 (d) 54
4. 4.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) 120 min (b) 54 min (c) 720 min (d) 6 min
5. 5.A teacher has 14 pencils and 18 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 14 (b) 1 (c) 2 (d) 4
6. 6.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) 20 (c) 4 (d) 2
7. 7.A teacher has 48 pencils and 60 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 48 (b) 12 (c) 240 (d) 6
8. 8.What is the smallest number of sweets that can be shared equally among 20 children or among 25 children, with none left over? (a) 200 (b) 100 (c) 500 (d) 45
9. 9.Two ribbons are 27 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) 3 cm (b) 9 cm (c) 27 cm (d) 36 cm
10. 10.What is the smallest number of sweets that can be shared equally among 6 children or among 8 children, with none left over? (a) 24 (b) 48 (c) 25 (d) 14
11. 11.What is the smallest number of sweets that can be shared equally among 6 children or among 15 children, with none left over? (a) 21 (b) 60 (c) 30 (d) 90
12. 12.What is the smallest number of sweets that can be shared equally among 15 children or among 35 children, with none left over? (a) 525 (b) 105 (c) 50 (d) 210
13. 13.A teacher has 18 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) 18 (c) 126 (d) 3
14. 14.A teacher has 8 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) 20 (c) 2 (d) 4
15. 15.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) 6 min (b) 216 min (c) 36 min (d) 30 min
16. 16.What is the smallest number of sweets that can be shared equally among 18 children or among 42 children, with none left over? (a) 756 (b) 60 (c) 252 (d) 126
17. 17.Two ribbons are 24 cm and 64 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) 40 cm (d) 24 cm
18. 18.Two ribbons are 28 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) 21 cm (b) 28 cm (c) 7 cm (d) 1 cm
19. 19.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
20. 20.A teacher has 44 pencils and 99 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 55 (b) 1 (c) 44 (d) 11
21. 21.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) 80 min (b) 18 min (c) 40 min (d) 2 min
22. 22.What is the smallest number of sweets that can be shared equally among 10 children or among 15 children, with none left over? (a) 30 (b) 150 (c) 60 (d) 25
23. 23.Two ribbons are 50 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) 40 cm (c) 10 cm (d) 50 cm
24. 24.Two ribbons are 24 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) 32 cm (b) 24 cm (c) 4 cm (d) 8 cm
25. 25.Two ribbons are 60 cm and 96 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) 60 cm (c) 36 cm (d) 12 cm
26. 26.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) 189 min (b) 3 min (c) 63 min (d) 30 min
27. 27.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) 50 cm (c) 10 cm (d) 30 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) 2 min (b) 48 min (c) 14 min (d) 24 min
29. 29.What is the smallest number of sweets that can be shared equally among 10 children or among 35 children, with none left over? (a) 140 (b) 350 (c) 45 (d) 70
30. 30.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) 5 min (c) 30 min (d) 150 min
31. 31.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) 224 min (d) 56 min
32. 32.A teacher has 27 pencils and 36 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 108 (c) 9 (d) 27
33. 33.A teacher has 4 pencils and 6 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 4 (b) 2 (c) 12 (d) 1
34. 34.Two ribbons are 22 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) 1 cm (b) 22 cm (c) 11 cm (d) 77 cm
35. 35.A teacher has 33 pencils and 55 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 11 (b) 1 (c) 33 (d) 22
36. 36.A teacher has 72 pencils and 81 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 648 (b) 72 (c) 3 (d) 9
37. 37.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) 2 min (c) 40 min (d) 20 min
38. 38.What is the smallest number of sweets that can be shared equally among 8 children or among 14 children, with none left over? (a) 112 (b) 22 (c) 56 (d) 57
39. 39.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) 40 min (b) 5 min (c) 75 min (d) 375 min
40. 40.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) 84 min (c) 54 min (d) 504 min

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