HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 18 · 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 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) 7 (b) 14 (c) 49 (d) 1
2. 2.What is the smallest number of sweets that can be shared equally among 8 children or among 20 children, with none left over? (a) 80 (b) 28 (c) 160 (d) 40
3. 3.Two ribbons are 60 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) 60 cm (b) 6 cm (c) 48 cm (d) 12 cm
4. 4.Two ribbons are 12 cm and 32 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) 20 cm (c) 2 cm (d) 4 cm
5. 5.What is the smallest number of sweets that can be shared equally among 12 children or among 15 children, with none left over? (a) 120 (b) 27 (c) 60 (d) 180
6. 6.Two ribbons are 14 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) 14 cm (c) 49 cm (d) 1 cm
7. 7.Two ribbons are 20 cm and 32 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) 20 cm (d) 4 cm
8. 8.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) 3 (b) 54 (c) 9 (d) 18
9. 9.Two ribbons are 24 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) 24 cm (b) 36 cm (c) 6 cm (d) 12 cm
10. 10.What is the smallest number of sweets that can be shared equally among 12 children or among 14 children, with none left over? (a) 85 (b) 26 (c) 84 (d) 168
11. 11.A teacher has 10 pencils and 35 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) 10 (d) 1
12. 12.What is the smallest number of sweets that can be shared equally among 20 children or among 24 children, with none left over? (a) 44 (b) 120 (c) 240 (d) 480
13. 13.A teacher has 21 pencils and 49 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) 1 (d) 21
14. 14.What is the smallest number of sweets that can be shared equally among 10 children or among 15 children, with none left over? (a) 30 (b) 25 (c) 60 (d) 150
15. 15.A teacher has 60 pencils and 84 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 60 (b) 12 (c) 24 (d) 6
16. 16.What is the smallest number of sweets that can be shared equally among 12 children or among 16 children, with none left over? (a) 48 (b) 96 (c) 192 (d) 28
17. 17.What is the smallest number of sweets that can be shared equally among 8 children or among 14 children, with none left over? (a) 112 (b) 56 (c) 57 (d) 22
18. 18.Two ribbons are 35 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
19. 19.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) 5 min (b) 25 min (c) 150 min (d) 30 min
20. 20.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) 1 cm (c) 11 cm (d) 33 cm
21. 21.Two ribbons are 12 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) 3 cm (b) 9 cm (c) 12 cm (d) 1 cm
22. 22.What is the smallest number of sweets that can be shared equally among 9 children or among 21 children, with none left over? (a) 189 (b) 30 (c) 63 (d) 126
23. 23.What is the smallest number of sweets that can be shared equally among 18 children or among 24 children, with none left over? (a) 42 (b) 144 (c) 72 (d) 432
24. 24.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) 1 (b) 2 (c) 16 (d) 144
25. 25.Two ribbons are 72 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) 72 cm (b) 504 cm (c) 12 cm (d) 6 cm
26. 26.Two bells ring every 8 minutes and every 12 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 20 min (b) 24 min (c) 96 min (d) 4 min
27. 27.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) 24 min (b) 14 min (c) 48 min (d) 2 min
28. 28.A teacher has 14 pencils and 35 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 14 (c) 7 (d) 21
29. 29.Two ribbons are 10 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) 5 cm (c) 10 cm (d) 25 cm
30. 30.A teacher has 20 pencils and 70 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 10 (b) 20 (c) 5 (d) 50
31. 31.What is the smallest number of sweets that can be shared equally among 15 children or among 25 children, with none left over? (a) 150 (b) 75 (c) 40 (d) 375
32. 32.A teacher has 22 pencils and 77 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) 11 (d) 55
33. 33.Two ribbons are 30 cm and 70 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) 10 cm (c) 30 cm (d) 40 cm
34. 34.Two bells ring every 20 minutes and every 25 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 500 min (b) 5 min (c) 45 min (d) 100 min
35. 35.A teacher has 84 pencils and 96 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 672 (c) 12 (d) 84
36. 36.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) 15 cm (b) 12 cm (c) 1 cm (d) 3 cm
37. 37.A teacher has 35 pencils and 49 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 35 (c) 7 (d) 14
38. 38.What is the smallest number of sweets that can be shared equally among 24 children or among 30 children, with none left over? (a) 720 (b) 120 (c) 240 (d) 54
39. 39.A teacher has 21 pencils and 56 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) 7 (d) 35
40. 40.A teacher has 27 pencils and 36 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 27 (c) 9 (d) 108

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