HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 2 · 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 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) 20 (b) 2 (c) 4 (d) 8
2. 2.A teacher has 15 pencils and 20 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 5 (b) 1 (c) 15 (d) 60
3. 3.What is the smallest number of sweets that can be shared equally among 15 children or among 35 children, with none left over? (a) 105 (b) 50 (c) 210 (d) 525
4. 4.Two ribbons are 18 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) 18 cm (b) 9 cm (c) 63 cm (d) 3 cm
5. 5.A teacher has 63 pencils and 72 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 504 (b) 3 (c) 9 (d) 63
6. 6.A teacher has 50 pencils and 60 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 300 (b) 10 (c) 5 (d) 50
7. 7.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) 5 min (b) 55 min (c) 140 min (d) 700 min
8. 8.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
9. 9.A teacher has 45 pencils and 72 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) 45 (d) 27
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) 48 (b) 25 (c) 24 (d) 14
11. 11.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) 25 min (d) 5 min
12. 12.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) 160 min (d) 4 min
13. 13.A teacher has 22 pencils and 33 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 22 (c) 66 (d) 11
14. 14.A teacher has 24 pencils and 84 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) 12 (d) 60
15. 15.A teacher has 50 pencils and 90 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 40 (b) 5 (c) 10 (d) 50
16. 16.Two ribbons are 9 cm and 12 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) 1 cm (c) 9 cm (d) 3 cm
17. 17.A teacher has 48 pencils and 56 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 4 (b) 336 (c) 48 (d) 8
18. 18.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) 8 (c) 1 (d) 10
19. 19.A teacher has 4 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) 2 (c) 4 (d) 1
20. 20.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) 9 (b) 18 (c) 54 (d) 3
21. 21.A teacher has 16 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) 16 (c) 1 (d) 144
22. 22.A teacher has 10 pencils and 45 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 10 (b) 1 (c) 35 (d) 5
23. 23.Two ribbons are 18 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) 1 cm (b) 126 cm (c) 18 cm (d) 3 cm
24. 24.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) 6 (c) 3 (d) 24
25. 25.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) 60 cm (b) 1 cm (c) 3 cm (d) 12 cm
26. 26.What is the smallest number of sweets that can be shared equally among 15 children or among 21 children, with none left over? (a) 105 (b) 36 (c) 315 (d) 210
27. 27.What is the smallest number of sweets that can be shared equally among 12 children or among 16 children, with none left over? (a) 96 (b) 192 (c) 28 (d) 48
28. 28.What is the smallest number of sweets that can be shared equally among 12 children or among 20 children, with none left over? (a) 120 (b) 32 (c) 240 (d) 60
29. 29.Two ribbons are 60 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) 360 cm (b) 12 cm (c) 60 cm (d) 6 cm
30. 30.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) 42 (c) 60 (d) 360
31. 31.What is the smallest number of sweets that can be shared equally among 6 children or among 10 children, with none left over? (a) 16 (b) 60 (c) 30 (d) 31
32. 32.Two ribbons are 35 cm and 42 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) 7 cm (c) 35 cm (d) 210 cm
33. 33.What is the smallest number of sweets that can be shared equally among 4 children or among 6 children, with none left over? (a) 13 (b) 10 (c) 24 (d) 12
34. 34.A teacher has 25 pencils and 30 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 25 (b) 5 (c) 1 (d) 150
35. 35.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
36. 36.Two bells ring every 15 minutes and every 35 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 5 min (b) 105 min (c) 525 min (d) 50 min
37. 37.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
38. 38.What is the smallest number of sweets that can be shared equally among 25 children or among 30 children, with none left over? (a) 750 (b) 150 (c) 55 (d) 300
39. 39.Two ribbons are 30 cm and 42 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) 30 cm (d) 12 cm
40. 40.Two ribbons are 48 cm and 60 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) 48 cm (c) 240 cm (d) 12 cm

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