HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 764 · 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 12 children or among 42 children, with none left over? (a) 54 (b) 168 (c) 504 (d) 84
2. 2.A teacher has 35 pencils and 63 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 28 (b) 35 (c) 1 (d) 7
3. 3.A teacher has 30 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) 24 (d) 3
4. 4.Two ribbons are 6 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) 6 cm (b) 3 cm (c) 9 cm (d) 1 cm
5. 5.What is the smallest number of sweets that can be shared equally among 4 children or among 14 children, with none left over? (a) 18 (b) 56 (c) 28 (d) 29
6. 6.A teacher has 10 pencils and 15 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 30 (b) 1 (c) 5 (d) 10
7. 7.Two ribbons are 33 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) 1 cm (c) 55 cm (d) 33 cm
8. 8.A teacher has 8 pencils and 20 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 12 (b) 2 (c) 4 (d) 8
9. 9.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) 12 (b) 144 (c) 36 (d) 6
10. 10.Two ribbons are 8 cm and 10 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 40 cm (b) 1 cm (c) 2 cm (d) 8 cm
11. 11.A teacher has 18 pencils and 63 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 18 (b) 3 (c) 45 (d) 9
12. 12.A teacher has 40 pencils and 70 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 5 (b) 30 (c) 10 (d) 40
13. 13.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
14. 14.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) 4 min (b) 336 min (c) 84 min (d) 40 min
15. 15.What is the smallest number of sweets that can be shared equally among 9 children or among 12 children, with none left over? (a) 21 (b) 72 (c) 36 (d) 108
16. 16.Two bells ring every 10 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 2 min (b) 70 min (c) 24 min (d) 140 min
17. 17.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) 5 min (d) 35 min
18. 18.Two ribbons are 36 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) 12 cm (b) 6 cm (c) 36 cm (d) 24 cm
19. 19.Two ribbons are 20 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) 2 cm (b) 16 cm (c) 4 cm (d) 20 cm
20. 20.Two ribbons are 88 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) 88 cm (b) 11 cm (c) 792 cm (d) 1 cm
21. 21.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) 75 min (d) 375 min
22. 22.Two ribbons are 36 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) 180 cm (b) 36 cm (c) 9 cm (d) 3 cm
23. 23.Two ribbons are 66 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) 11 cm (b) 66 cm (c) 462 cm (d) 1 cm
24. 24.Two ribbons are 9 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) 6 cm (b) 3 cm (c) 9 cm (d) 1 cm
25. 25.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) 48 min (b) 24 min (c) 14 min (d) 2 min
26. 26.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
27. 27.A teacher has 18 pencils and 24 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 18 (c) 6 (d) 72
28. 28.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) 6 cm (b) 360 cm (c) 60 cm (d) 12 cm
29. 29.What is the smallest number of sweets that can be shared equally among 24 children or among 30 children, with none left over? (a) 240 (b) 54 (c) 120 (d) 720
30. 30.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) 40 min (d) 20 min
31. 31.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) 2 min (b) 42 min (c) 84 min (d) 20 min
32. 32.Two bells ring every 12 minutes and every 18 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 36 min (b) 216 min (c) 30 min (d) 6 min
33. 33.What is the smallest number of sweets that can be shared equally among 12 children or among 28 children, with none left over? (a) 84 (b) 336 (c) 40 (d) 168
34. 34.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) 168 (b) 24 (c) 4 (d) 2
35. 35.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) 27 min (b) 42 min (c) 126 min (d) 3 min
36. 36.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) 10 min (d) 24 min
37. 37.A teacher has 16 pencils and 20 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 4 (b) 80 (c) 16 (d) 2
38. 38.Two ribbons are 16 cm and 20 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) 80 cm (d) 2 cm
39. 39.Two ribbons are 12 cm and 20 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) 4 cm (d) 8 cm
40. 40.Two bells ring every 8 minutes and every 28 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 224 min (b) 56 min (c) 36 min (d) 4 min

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