HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 512 · 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 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) 42 min (b) 72 min (c) 432 min (d) 6 min
2. 2.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) 3 (c) 54 (d) 18
3. 3.A teacher has 24 pencils and 42 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 24 (b) 3 (c) 6 (d) 18
4. 4.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) 1 (b) 30 (c) 10 (d) 5
5. 5.Two ribbons are 48 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) 3 cm (b) 6 cm (c) 432 cm (d) 48 cm
6. 6.Two ribbons are 6 cm and 8 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) 2 cm (c) 24 cm (d) 1 cm
7. 7.Two bells ring every 12 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 33 min (b) 84 min (c) 3 min (d) 252 min
8. 8.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) 72 (c) 144 (d) 432
9. 9.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) 140 min (b) 70 min (c) 2 min (d) 24 min
10. 10.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) 18 (c) 28 (d) 29
11. 11.A teacher has 12 pencils and 18 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 36 (b) 3 (c) 12 (d) 6
12. 12.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) 40 min (b) 375 min (c) 75 min (d) 5 min
13. 13.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) 525 min (b) 105 min (c) 5 min (d) 50 min
14. 14.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
15. 15.What is the smallest number of sweets that can be shared equally among 6 children or among 9 children, with none left over? (a) 36 (b) 18 (c) 54 (d) 15
16. 16.What is the smallest number of sweets that can be shared equally among 8 children or among 14 children, with none left over? (a) 22 (b) 56 (c) 57 (d) 112
17. 17.A teacher has 18 pencils and 42 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 18 (b) 6 (c) 24 (d) 3
18. 18.What is the smallest number of sweets that can be shared equally among 6 children or among 14 children, with none left over? (a) 20 (b) 84 (c) 42 (d) 43
19. 19.A teacher has 6 pencils and 16 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 10 (c) 2 (d) 1
20. 20.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
21. 21.Two ribbons are 14 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) 7 cm (b) 1 cm (c) 14 cm (d) 21 cm
22. 22.Two ribbons are 44 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) 1 cm (b) 11 cm (c) 33 cm (d) 44 cm
23. 23.Two bells ring every 12 minutes and every 20 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 240 min (b) 60 min (c) 32 min (d) 4 min
24. 24.What is the smallest number of sweets that can be shared equally among 15 children or among 20 children, with none left over? (a) 35 (b) 300 (c) 60 (d) 120
25. 25.A teacher has 16 pencils and 56 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 40 (b) 8 (c) 16 (d) 4
26. 26.Two bells ring every 16 minutes and every 28 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 4 min (b) 448 min (c) 44 min (d) 112 min
27. 27.What is the smallest number of sweets that can be shared equally among 16 children or among 20 children, with none left over? (a) 80 (b) 320 (c) 160 (d) 36
28. 28.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) 20 min (b) 2 min (c) 42 min (d) 84 min
29. 29.Two ribbons are 15 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) 15 cm (c) 3 cm (d) 90 cm
30. 30.A teacher has 60 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) 60 (c) 36 (d) 12
31. 31.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) 16 (c) 2 (d) 144
32. 32.A teacher has 6 pencils and 14 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 8 (b) 6 (c) 1 (d) 2
33. 33.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) 1 (b) 10 (c) 2 (d) 8
34. 34.Two ribbons are 20 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) 25 cm (b) 1 cm (c) 20 cm (d) 5 cm
35. 35.A teacher has 12 pencils and 14 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 12 (b) 84 (c) 1 (d) 2
36. 36.A teacher has 66 pencils and 77 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 462 (b) 1 (c) 66 (d) 11
37. 37.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) 5 min (b) 45 min (c) 70 min (d) 350 min
38. 38.Two ribbons are 16 cm and 24 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) 48 cm (c) 16 cm (d) 8 cm
39. 39.A teacher has 28 pencils and 36 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 8 (b) 28 (c) 2 (d) 4
40. 40.Two ribbons are 8 cm and 14 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) 6 cm (c) 8 cm (d) 1 cm

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