HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 413 · 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.What is the smallest number of sweets that can be shared equally among 4 children or among 14 children, with none left over? (a) 56 (b) 29 (c) 18 (d) 28
2. 2.Two ribbons are 14 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) 14 cm (b) 35 cm (c) 7 cm (d) 1 cm
3. 3.Two ribbons are 12 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) 6 cm (b) 12 cm (c) 18 cm (d) 3 cm
4. 4.A teacher has 10 pencils and 18 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 2 (b) 10 (c) 8 (d) 1
5. 5.Two ribbons are 40 cm and 45 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 360 cm (b) 1 cm (c) 40 cm (d) 5 cm
6. 6.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) 120 min (c) 44 min (d) 4 min
7. 7.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) 42 min (b) 360 min (c) 60 min (d) 6 min
8. 8.Two ribbons are 12 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) 1 cm (b) 12 cm (c) 3 cm (d) 60 cm
9. 9.Two ribbons are 9 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) 12 cm (b) 1 cm (c) 3 cm (d) 9 cm
10. 10.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) 24 cm (c) 40 cm (d) 8 cm
11. 11.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) 5 min (b) 300 min (c) 35 min (d) 60 min
12. 12.A teacher has 44 pencils and 77 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 44 (b) 11 (c) 33 (d) 1
13. 13.What is the smallest number of sweets that can be shared equally among 16 children or among 20 children, with none left over? (a) 160 (b) 80 (c) 320 (d) 36
14. 14.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) 27 min (c) 42 min (d) 3 min
15. 15.What is the smallest number of sweets that can be shared equally among 8 children or among 12 children, with none left over? (a) 96 (b) 20 (c) 48 (d) 24
16. 16.What is the smallest number of sweets that can be shared equally among 6 children or among 14 children, with none left over? (a) 42 (b) 43 (c) 20 (d) 84
17. 17.What is the smallest number of sweets that can be shared equally among 6 children or among 10 children, with none left over? (a) 60 (b) 16 (c) 31 (d) 30
18. 18.Two ribbons are 15 cm and 25 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) 1 cm (c) 15 cm (d) 10 cm
19. 19.What is the smallest number of sweets that can be shared equally among 10 children or among 14 children, with none left over? (a) 70 (b) 71 (c) 140 (d) 24
20. 20.Two bells ring every 12 minutes and every 15 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 27 min (b) 3 min (c) 60 min (d) 180 min
21. 21.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) 375 min (b) 75 min (c) 5 min (d) 40 min
22. 22.Two ribbons are 48 cm and 84 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) 36 cm (c) 12 cm (d) 48 cm
23. 23.A teacher has 20 pencils and 45 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 20 (b) 1 (c) 25 (d) 5
24. 24.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) 90 (c) 60 (d) 30
25. 25.Two ribbons are 24 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) 168 cm (c) 24 cm (d) 2 cm
26. 26.Two ribbons are 84 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) 6 cm (b) 84 cm (c) 24 cm (d) 12 cm
27. 27.Two ribbons are 42 cm and 48 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 42 cm (b) 3 cm (c) 336 cm (d) 6 cm
28. 28.Two bells ring every 6 minutes and every 15 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 3 min (b) 90 min (c) 30 min (d) 21 min
29. 29.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) 24 min (c) 14 min (d) 48 min
30. 30.A teacher has 21 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
31. 31.Two ribbons are 35 cm and 40 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) 280 cm (c) 35 cm (d) 1 cm
32. 32.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
33. 33.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) 33 (b) 11 (c) 22 (d) 1
34. 34.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) 28 min (b) 40 min (c) 4 min (d) 160 min
35. 35.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
36. 36.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) 42 (c) 6 (d) 12
37. 37.What is the smallest number of sweets that can be shared equally among 12 children or among 30 children, with none left over? (a) 360 (b) 42 (c) 60 (d) 120
38. 38.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) 18 (d) 15
39. 39.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) 350 min (b) 45 min (c) 70 min (d) 5 min
40. 40.What is the smallest number of sweets that can be shared equally among 10 children or among 15 children, with none left over? (a) 150 (b) 60 (c) 30 (d) 25

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