HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 211 · 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.Two ribbons are 21 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) 84 cm (b) 21 cm (c) 7 cm (d) 1 cm
2. 2.A teacher has 20 pencils and 50 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 30 (b) 5 (c) 10 (d) 20
3. 3.Two bells ring every 6 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 42 min (b) 20 min (c) 2 min (d) 84 min
4. 4.Two ribbons are 36 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
5. 5.What is the smallest number of sweets that can be shared equally among 15 children or among 35 children, with none left over? (a) 50 (b) 210 (c) 105 (d) 525
6. 6.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) 252 min (b) 33 min (c) 3 min (d) 84 min
7. 7.A teacher has 24 pencils and 54 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 30 (b) 24 (c) 6 (d) 3
8. 8.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) 108 min (b) 36 min (c) 21 min (d) 3 min
9. 9.A teacher has 8 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) 2 (c) 6 (d) 8
10. 10.Two ribbons are 32 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) 4 cm (b) 32 cm (c) 160 cm (d) 8 cm
11. 11.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) 5 min (b) 750 min (c) 55 min (d) 150 min
12. 12.A teacher has 49 pencils and 63 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 7 (b) 1 (c) 14 (d) 49
13. 13.A teacher has 36 pencils and 84 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 48 (b) 36 (c) 12 (d) 6
14. 14.Two ribbons are 48 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) 4 cm (b) 48 cm (c) 336 cm (d) 8 cm
15. 15.A teacher has 24 pencils and 64 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 40 (b) 24 (c) 8 (d) 4
16. 16.A teacher has 24 pencils and 108 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 24 (c) 84 (d) 12
17. 17.A teacher has 48 pencils and 54 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 48 (b) 432 (c) 3 (d) 6
18. 18.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) 42 (c) 27 (d) 84
19. 19.Two ribbons are 15 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) 20 cm (b) 15 cm (c) 1 cm (d) 5 cm
20. 20.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) 54 min (b) 3 min (c) 18 min (d) 15 min
21. 21.What is the smallest number of sweets that can be shared equally among 10 children or among 14 children, with none left over? (a) 140 (b) 24 (c) 70 (d) 71
22. 22.A teacher has 45 pencils and 81 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 45 (b) 9 (c) 3 (d) 36
23. 23.What is the smallest number of sweets that can be shared equally among 6 children or among 9 children, with none left over? (a) 15 (b) 36 (c) 54 (d) 18
24. 24.What is the smallest number of sweets that can be shared equally among 4 children or among 6 children, with none left over? (a) 10 (b) 12 (c) 13 (d) 24
25. 25.Two bells ring every 6 minutes and every 10 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 60 min (b) 16 min (c) 30 min (d) 2 min
26. 26.Two bells ring every 12 minutes and every 28 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 84 min (b) 40 min (c) 336 min (d) 4 min
27. 27.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) 12 cm (c) 16 cm (d) 4 cm
28. 28.Two ribbons are 36 cm and 81 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 45 cm (b) 9 cm (c) 3 cm (d) 36 cm
29. 29.Two ribbons are 4 cm and 10 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) 6 cm (c) 4 cm (d) 2 cm
30. 30.Two ribbons are 10 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) 1 cm (b) 10 cm (c) 5 cm (d) 35 cm
31. 31.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) 36 cm (b) 3 cm (c) 27 cm (d) 9 cm
32. 32.Two bells ring every 12 minutes and every 20 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 240 min (b) 4 min (c) 60 min (d) 32 min
33. 33.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) 30 (d) 31
34. 34.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) 140 min (b) 24 min (c) 2 min (d) 70 min
35. 35.What is the smallest number of sweets that can be shared equally among 4 children or among 10 children, with none left over? (a) 20 (b) 40 (c) 14 (d) 21
36. 36.Two ribbons are 24 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) 12 cm (c) 24 cm (d) 60 cm
37. 37.What is the smallest number of sweets that can be shared equally among 12 children or among 21 children, with none left over? (a) 33 (b) 252 (c) 168 (d) 84
38. 38.A teacher has 18 pencils and 63 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 18 (b) 45 (c) 9 (d) 3
39. 39.Two bells ring every 18 minutes and every 42 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 126 min (b) 6 min (c) 756 min (d) 60 min
40. 40.What is the smallest number of sweets that can be shared equally among 12 children or among 30 children, with none left over? (a) 120 (b) 360 (c) 60 (d) 42

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