HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 173 · 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 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) 3 (b) 18 (c) 45 (d) 9
2. 2.What is the smallest number of sweets that can be shared equally among 8 children or among 28 children, with none left over? (a) 56 (b) 224 (c) 112 (d) 36
3. 3.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) 35 cm (d) 14 cm
4. 4.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) 66 (b) 462 (c) 1 (d) 11
5. 5.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) 50 min (b) 35 min (c) 250 min (d) 5 min
6. 6.A teacher has 6 pencils and 27 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 21 (c) 3 (d) 1
7. 7.Two ribbons are 9 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) 1 cm (b) 12 cm (c) 3 cm (d) 9 cm
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) 4 min (b) 84 min (c) 40 min (d) 336 min
9. 9.Two bells ring every 20 minutes and every 24 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 480 min (b) 120 min (c) 4 min (d) 44 min
10. 10.Two ribbons are 64 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) 576 cm (b) 8 cm (c) 64 cm (d) 4 cm
11. 11.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) 56 min (b) 4 min (c) 36 min (d) 224 min
12. 12.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) 60 (c) 27 (d) 180
13. 13.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) 32 min (b) 240 min (c) 60 min (d) 4 min
14. 14.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
15. 15.A teacher has 15 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) 15 (c) 1 (d) 9
16. 16.A teacher has 49 pencils and 56 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 49 (b) 392 (c) 1 (d) 7
17. 17.Two ribbons are 6 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) 6 cm (b) 1 cm (c) 21 cm (d) 3 cm
18. 18.Two ribbons are 84 cm and 96 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 672 cm (b) 84 cm (c) 12 cm (d) 6 cm
19. 19.A teacher has 20 pencils and 28 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 8 (b) 4 (c) 2 (d) 20
20. 20.A teacher has 45 pencils and 81 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 45 (c) 36 (d) 9
21. 21.Two bells ring every 20 minutes and every 35 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 55 min (b) 5 min (c) 140 min (d) 700 min
22. 22.Two bells ring every 6 minutes and every 9 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 15 min (b) 54 min (c) 18 min (d) 3 min
23. 23.Two bells ring every 12 minutes and every 42 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 6 min (b) 54 min (c) 504 min (d) 84 min
24. 24.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) 28 min (b) 4 min (c) 40 min (d) 160 min
25. 25.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) 375 min (b) 75 min (c) 40 min (d) 5 min
26. 26.What is the smallest number of sweets that can be shared equally among 6 children or among 10 children, with none left over? (a) 60 (b) 31 (c) 16 (d) 30
27. 27.Two ribbons are 12 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) 12 cm (c) 16 cm (d) 4 cm
28. 28.What is the smallest number of sweets that can be shared equally among 25 children or among 30 children, with none left over? (a) 55 (b) 750 (c) 150 (d) 300
29. 29.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) 8 cm (b) 2 cm (c) 6 cm (d) 1 cm
30. 30.Two ribbons are 28 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) 8 cm (b) 2 cm (c) 4 cm (d) 28 cm
31. 31.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) 9 (b) 180 (c) 36 (d) 3
32. 32.Two bells ring every 12 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 168 min (b) 2 min (c) 26 min (d) 84 min
33. 33.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) 30 (b) 40 (c) 5 (d) 10
34. 34.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
35. 35.Two bells ring every 25 minutes and every 30 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 750 min (b) 55 min (c) 150 min (d) 5 min
36. 36.What is the smallest number of sweets that can be shared equally among 6 children or among 9 children, with none left over? (a) 15 (b) 54 (c) 36 (d) 18
37. 37.A teacher has 14 pencils and 21 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 42 (c) 14 (d) 7
38. 38.What is the smallest number of sweets that can be shared equally among 18 children or among 21 children, with none left over? (a) 39 (b) 126 (c) 252 (d) 378
39. 39.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) 54 min (b) 6 min (c) 120 min (d) 720 min
40. 40.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) 80 (b) 2 (c) 4 (d) 16

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