HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 263 · 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 55 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) 44 cm (b) 55 cm (c) 11 cm (d) 1 cm
2. 2.What is the smallest number of sweets that can be shared equally among 9 children or among 21 children, with none left over? (a) 30 (b) 189 (c) 126 (d) 63
3. 3.What is the smallest number of sweets that can be shared equally among 8 children or among 28 children, with none left over? (a) 36 (b) 224 (c) 112 (d) 56
4. 4.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) 60 cm (b) 6 cm (c) 24 cm (d) 12 cm
5. 5.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) 84 min (b) 2 min (c) 42 min (d) 20 min
6. 6.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
7. 7.Two bells ring every 6 minutes and every 15 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 30 min (b) 90 min (c) 3 min (d) 21 min
8. 8.Two ribbons are 50 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) 5 cm (b) 300 cm (c) 50 cm (d) 10 cm
9. 9.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) 336 min (c) 4 min (d) 40 min
10. 10.Two bells ring every 15 minutes and every 25 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 5 min (b) 40 min (c) 375 min (d) 75 min
11. 11.A teacher has 15 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) 1 (c) 15 (d) 12
12. 12.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) 1 (c) 21 (d) 7
13. 13.What is the smallest number of sweets that can be shared equally among 4 children or among 14 children, with none left over? (a) 56 (b) 28 (c) 29 (d) 18
14. 14.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) 84 (c) 252 (d) 33
15. 15.Two bells ring every 10 minutes and every 35 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 45 min (b) 5 min (c) 70 min (d) 350 min
16. 16.A teacher has 4 pencils and 10 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) 4 (d) 2
17. 17.A teacher has 44 pencils and 77 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 11 (b) 33 (c) 1 (d) 44
18. 18.A teacher has 10 pencils and 14 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 10 (b) 4 (c) 1 (d) 2
19. 19.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) 20 (b) 10 (c) 5 (d) 60
20. 20.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) 40 min (c) 4 min (d) 28 min
21. 21.What is the smallest number of sweets that can be shared equally among 6 children or among 15 children, with none left over? (a) 90 (b) 60 (c) 30 (d) 21
22. 22.Two ribbons are 12 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) 3 cm (b) 36 cm (c) 12 cm (d) 6 cm
23. 23.Two ribbons are 18 cm and 48 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) 18 cm (d) 6 cm
24. 24.What is the smallest number of sweets that can be shared equally among 12 children or among 30 children, with none left over? (a) 360 (b) 42 (c) 120 (d) 60
25. 25.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) 24 min (c) 20 min (d) 4 min
26. 26.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) 50 (b) 40 (c) 10 (d) 5
27. 27.Two ribbons are 4 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) 1 cm (b) 2 cm (c) 4 cm (d) 14 cm
28. 28.Two bells ring every 4 minutes and every 6 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 12 min (b) 2 min (c) 24 min (d) 10 min
29. 29.What is the smallest number of sweets that can be shared equally among 20 children or among 28 children, with none left over? (a) 560 (b) 280 (c) 140 (d) 48
30. 30.What is the smallest number of sweets that can be shared equally among 12 children or among 42 children, with none left over? (a) 504 (b) 84 (c) 54 (d) 168
31. 31.A teacher has 9 pencils and 12 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 9 (c) 3 (d) 36
32. 32.What is the smallest number of sweets that can be shared equally among 8 children or among 12 children, with none left over? (a) 24 (b) 48 (c) 20 (d) 96
33. 33.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) 1 (b) 18 (c) 6 (d) 3
34. 34.Two bells ring every 24 minutes and every 30 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 6 min (b) 120 min (c) 720 min (d) 54 min
35. 35.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) 4 (c) 1 (d) 2
36. 36.A teacher has 42 pencils and 48 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 336 (c) 6 (d) 42
37. 37.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) 180 (c) 27 (d) 60
38. 38.Two ribbons are 48 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) 48 cm (b) 36 cm (c) 6 cm (d) 12 cm
39. 39.Two ribbons are 36 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) 9 cm (b) 27 cm (c) 3 cm (d) 36 cm
40. 40.Two ribbons are 8 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) 20 cm (c) 4 cm (d) 8 cm

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