HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 6 · 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 16 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) 16 cm (b) 4 cm (c) 2 cm (d) 20 cm
2. 2.A teacher has 21 pencils and 28 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 84 (b) 21 (c) 1 (d) 7
3. 3.What is the smallest number of sweets that can be shared equally among 10 children or among 35 children, with none left over? (a) 45 (b) 140 (c) 70 (d) 350
4. 4.What is the smallest number of sweets that can be shared equally among 12 children or among 20 children, with none left over? (a) 240 (b) 60 (c) 32 (d) 120
5. 5.What is the smallest number of sweets that can be shared equally among 9 children or among 15 children, with none left over? (a) 90 (b) 45 (c) 24 (d) 135
6. 6.A teacher has 32 pencils and 36 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 32 (b) 288 (c) 2 (d) 4
7. 7.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) 3 min (b) 42 min (c) 27 min (d) 126 min
8. 8.What is the smallest number of sweets that can be shared equally among 12 children or among 18 children, with none left over? (a) 72 (b) 216 (c) 30 (d) 36
9. 9.Two ribbons are 6 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) 1 cm (c) 6 cm (d) 2 cm
10. 10.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) 60 (c) 360 (d) 42
11. 11.Two ribbons are 45 cm and 72 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) 45 cm (c) 27 cm (d) 9 cm
12. 12.Two bells ring every 15 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 3 min (b) 36 min (c) 315 min (d) 105 min
13. 13.Two ribbons are 72 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) 3 cm (b) 72 cm (c) 9 cm (d) 648 cm
14. 14.A teacher has 30 pencils and 42 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 12 (b) 30 (c) 6 (d) 3
15. 15.A teacher has 24 pencils and 28 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) 24 (d) 168
16. 16.Two ribbons are 4 cm and 14 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) 2 cm (d) 4 cm
17. 17.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) 55 min (c) 150 min (d) 750 min
18. 18.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) 50 cm (d) 10 cm
19. 19.A teacher has 18 pencils and 27 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 54 (b) 9 (c) 3 (d) 18
20. 20.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) 30 min (b) 150 min (c) 5 min (d) 25 min
21. 21.A teacher has 8 pencils and 10 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) 1 (d) 2
22. 22.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) 9 (b) 3 (c) 27 (d) 18
23. 23.Two ribbons are 25 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) 25 cm (b) 5 cm (c) 1 cm (d) 20 cm
24. 24.Two ribbons are 60 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) 60 cm (c) 24 cm (d) 12 cm
25. 25.Two ribbons are 20 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) 15 cm (b) 20 cm (c) 5 cm (d) 1 cm
26. 26.A teacher has 18 pencils and 30 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 6 (c) 18 (d) 12
27. 27.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) 7 cm (b) 35 cm (c) 1 cm (d) 28 cm
28. 28.Two ribbons are 12 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) 1 cm (b) 15 cm (c) 12 cm (d) 3 cm
29. 29.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) 22 (c) 61 (d) 120
30. 30.Two ribbons are 14 cm and 18 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) 2 cm (c) 1 cm (d) 14 cm
31. 31.Two ribbons are 6 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) 3 cm (c) 1 cm (d) 15 cm
32. 32.What is the smallest number of sweets that can be shared equally among 15 children or among 21 children, with none left over? (a) 315 (b) 210 (c) 105 (d) 36
33. 33.Two ribbons are 6 cm and 9 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) 6 cm (c) 3 cm (d) 1 cm
34. 34.Two ribbons are 14 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) 14 cm (b) 42 cm (c) 7 cm (d) 1 cm
35. 35.A teacher has 15 pencils and 18 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 3 (c) 90 (d) 15
36. 36.Two ribbons are 77 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) 11 cm (b) 77 cm (c) 1 cm (d) 616 cm
37. 37.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) 36 (c) 80 (d) 320
38. 38.Two bells ring every 4 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 56 min (b) 2 min (c) 28 min (d) 18 min
39. 39.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) 1 (b) 20 (c) 5 (d) 25
40. 40.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) 35 cm (b) 1 cm (c) 14 cm (d) 7 cm

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