HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 913 · 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 10 children or among 15 children, with none left over? (a) 150 (b) 60 (c) 25 (d) 30
2. 2.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) 44 cm (b) 11 cm (c) 1 cm (d) 33 cm
3. 3.A teacher has 27 pencils and 45 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 27 (b) 9 (c) 3 (d) 18
4. 4.What is the smallest number of sweets that can be shared equally among 18 children or among 21 children, with none left over? (a) 126 (b) 378 (c) 39 (d) 252
5. 5.What is the smallest number of sweets that can be shared equally among 8 children or among 20 children, with none left over? (a) 28 (b) 40 (c) 80 (d) 160
6. 6.Two ribbons are 21 cm and 27 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) 1 cm (c) 3 cm (d) 21 cm
7. 7.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) 11 cm (b) 77 cm (c) 22 cm (d) 1 cm
8. 8.Two ribbons are 15 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) 6 cm (b) 15 cm (c) 3 cm (d) 1 cm
9. 9.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) 33 min (b) 3 min (c) 252 min (d) 84 min
10. 10.Two ribbons are 36 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) 180 cm (b) 36 cm (c) 9 cm (d) 3 cm
11. 11.What is the smallest number of sweets that can be shared equally among 6 children or among 21 children, with none left over? (a) 126 (b) 84 (c) 27 (d) 42
12. 12.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) 3 min (c) 18 min (d) 54 min
13. 13.What is the smallest number of sweets that can be shared equally among 10 children or among 12 children, with none left over? (a) 60 (b) 120 (c) 22 (d) 61
14. 14.Two bells ring every 10 minutes and every 12 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 60 min (b) 22 min (c) 2 min (d) 120 min
15. 15.Two bells ring every 12 minutes and every 16 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 192 min (b) 28 min (c) 48 min (d) 4 min
16. 16.A teacher has 40 pencils and 56 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 40 (b) 16 (c) 8 (d) 4
17. 17.A teacher has 20 pencils and 35 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 15 (b) 5 (c) 20 (d) 1
18. 18.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) 1 (d) 33
19. 19.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) 24 cm (b) 4 cm (c) 8 cm (d) 32 cm
20. 20.Two ribbons are 27 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) 27 cm (b) 108 cm (c) 9 cm (d) 3 cm
21. 21.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) 20 min (c) 2 min (d) 40 min
22. 22.What is the smallest number of sweets that can be shared equally among 12 children or among 28 children, with none left over? (a) 168 (b) 84 (c) 336 (d) 40
23. 23.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) 42 cm (b) 294 cm (c) 1 cm (d) 7 cm
24. 24.Two ribbons are 12 cm and 54 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) 6 cm (c) 42 cm (d) 3 cm
25. 25.What is the smallest number of sweets that can be shared equally among 20 children or among 35 children, with none left over? (a) 700 (b) 280 (c) 55 (d) 140
26. 26.A teacher has 14 pencils and 63 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 49 (b) 1 (c) 7 (d) 14
27. 27.Two ribbons are 18 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) 18 cm (b) 45 cm (c) 9 cm (d) 3 cm
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) 6 min (c) 72 min (d) 42 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) 14 min (b) 2 min (c) 24 min (d) 48 min
30. 30.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) 6 min (c) 60 min (d) 360 min
31. 31.Two ribbons are 30 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) 30 cm (c) 210 cm (d) 5 cm
32. 32.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) 126 min (b) 378 min (c) 39 min (d) 3 min
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) 12 (b) 1 (c) 4 (d) 2
34. 34.A teacher has 12 pencils and 27 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 12 (b) 15 (c) 1 (d) 3
35. 35.What is the smallest number of sweets that can be shared equally among 15 children or among 20 children, with none left over? (a) 60 (b) 120 (c) 35 (d) 300
36. 36.A teacher has 35 pencils and 63 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 28 (b) 7 (c) 35 (d) 1
37. 37.A teacher has 12 pencils and 14 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 84 (c) 12 (d) 2
38. 38.A teacher has 18 pencils and 24 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 18 (c) 6 (d) 72
39. 39.A teacher has 24 pencils and 36 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 24 (b) 72 (c) 6 (d) 12
40. 40.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) 3 cm (b) 6 cm (c) 12 cm (d) 18 cm

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