HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 441 · 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 9 children or among 12 children, with none left over? (a) 72 (b) 108 (c) 21 (d) 36
2. 2.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) 7 cm (b) 1 cm (c) 14 cm (d) 35 cm
3. 3.Two ribbons are 44 cm and 55 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) 44 cm (c) 11 cm (d) 220 cm
4. 4.What is the smallest number of sweets that can be shared equally among 4 children or among 10 children, with none left over? (a) 21 (b) 14 (c) 20 (d) 40
5. 5.A teacher has 36 pencils and 48 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 144 (b) 6 (c) 36 (d) 12
6. 6.A teacher has 6 pencils and 15 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 9 (b) 1 (c) 3 (d) 6
7. 7.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) 160 min (b) 28 min (c) 40 min (d) 4 min
8. 8.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) 336 min (b) 84 min (c) 40 min (d) 4 min
9. 9.A teacher has 20 pencils and 25 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) 100
10. 10.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) 5 cm (c) 20 cm (d) 1 cm
11. 11.A teacher has 33 pencils and 44 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 132 (c) 11 (d) 33
12. 12.Two bells ring every 8 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 112 min (b) 2 min (c) 56 min (d) 22 min
13. 13.What is the smallest number of sweets that can be shared equally among 12 children or among 21 children, with none left over? (a) 168 (b) 252 (c) 84 (d) 33
14. 14.Two ribbons are 25 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) 10 cm (b) 5 cm (c) 1 cm (d) 25 cm
15. 15.Two ribbons are 16 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) 4 cm (b) 56 cm (c) 16 cm (d) 8 cm
16. 16.A teacher has 44 pencils and 55 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 220 (c) 44 (d) 11
17. 17.What is the smallest number of sweets that can be shared equally among 12 children or among 14 children, with none left over? (a) 168 (b) 85 (c) 84 (d) 26
18. 18.A teacher has 70 pencils and 90 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 5 (b) 20 (c) 70 (d) 10
19. 19.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) 96 min (b) 4 min (c) 24 min (d) 20 min
20. 20.Two ribbons are 44 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) 55 cm (b) 44 cm (c) 1 cm (d) 11 cm
21. 21.What is the smallest number of sweets that can be shared equally among 12 children or among 20 children, with none left over? (a) 60 (b) 120 (c) 240 (d) 32
22. 22.What is the smallest number of sweets that can be shared equally among 8 children or among 12 children, with none left over? (a) 48 (b) 24 (c) 20 (d) 96
23. 23.Two bells ring every 10 minutes and every 25 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 250 min (b) 50 min (c) 35 min (d) 5 min
24. 24.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) 1 cm (b) 6 cm (c) 18 cm (d) 3 cm
25. 25.A teacher has 6 pencils and 9 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 1 (c) 18 (d) 3
26. 26.A teacher has 36 pencils and 45 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 180 (b) 9 (c) 36 (d) 3
27. 27.A teacher has 12 pencils and 15 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 12 (c) 60 (d) 3
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) 72 min (b) 42 min (c) 6 min (d) 432 min
29. 29.A teacher has 14 pencils and 16 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 112 (b) 2 (c) 1 (d) 14
30. 30.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) 18 cm (b) 1 cm (c) 126 cm (d) 3 cm
31. 31.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) 2 min (b) 14 min (c) 20 min (d) 40 min
32. 32.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) 4 (c) 2 (d) 8
33. 33.A teacher has 20 pencils and 30 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 5 (b) 20 (c) 10 (d) 60
34. 34.What is the smallest number of sweets that can be shared equally among 15 children or among 25 children, with none left over? (a) 75 (b) 150 (c) 375 (d) 40
35. 35.Two ribbons are 30 cm and 50 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) 20 cm (c) 5 cm (d) 30 cm
36. 36.Two ribbons are 30 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) 30 cm (b) 3 cm (c) 24 cm (d) 6 cm
37. 37.Two ribbons are 33 cm and 44 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 33 cm (b) 11 cm (c) 132 cm (d) 1 cm
38. 38.What is the smallest number of sweets that can be shared equally among 15 children or among 20 children, with none left over? (a) 120 (b) 60 (c) 300 (d) 35
39. 39.What is the smallest number of sweets that can be shared equally among 9 children or among 21 children, with none left over? (a) 63 (b) 30 (c) 126 (d) 189
40. 40.A teacher has 10 pencils and 12 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 2 (b) 60 (c) 10 (d) 1

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