HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 388 · 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 12 pencils and 21 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 12 (b) 3 (c) 1 (d) 9
2. 2.Two ribbons are 12 cm and 16 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) 4 cm (c) 12 cm (d) 2 cm
3. 3.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
4. 4.What is the smallest number of sweets that can be shared equally among 4 children or among 6 children, with none left over? (a) 12 (b) 24 (c) 10 (d) 13
5. 5.Two ribbons are 24 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) 6 cm (b) 24 cm (c) 12 cm (d) 60 cm
6. 6.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) 168 (c) 40 (d) 336
7. 7.What is the smallest number of sweets that can be shared equally among 20 children or among 24 children, with none left over? (a) 480 (b) 44 (c) 240 (d) 120
8. 8.A teacher has 72 pencils and 84 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 504 (b) 6 (c) 72 (d) 12
9. 9.Two ribbons are 6 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) 2 cm (b) 6 cm (c) 1 cm (d) 4 cm
10. 10.Two ribbons are 10 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) 10 cm (c) 4 cm (d) 1 cm
11. 11.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) 60 (c) 300 (d) 120
12. 12.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) 2 (c) 4 (d) 1
13. 13.A teacher has 12 pencils and 28 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 16 (b) 4 (c) 2 (d) 12
14. 14.Two bells ring every 9 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 189 min (b) 3 min (c) 63 min (d) 30 min
15. 15.What is the smallest number of sweets that can be shared equally among 10 children or among 14 children, with none left over? (a) 140 (b) 70 (c) 24 (d) 71
16. 16.Two bells ring every 18 minutes and every 30 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 48 min (b) 6 min (c) 90 min (d) 540 min
17. 17.What is the smallest number of sweets that can be shared equally among 18 children or among 30 children, with none left over? (a) 180 (b) 540 (c) 48 (d) 90
18. 18.Two bells ring every 10 minutes and every 15 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 30 min (b) 150 min (c) 25 min (d) 5 min
19. 19.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) 112 min (b) 448 min (c) 44 min (d) 4 min
20. 20.A teacher has 24 pencils and 60 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 24 (b) 36 (c) 12 (d) 6
21. 21.Two bells ring every 15 minutes and every 20 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 60 min (b) 5 min (c) 300 min (d) 35 min
22. 22.A teacher has 22 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) 11 (c) 22 (d) 33
23. 23.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) 14 min (b) 2 min (c) 20 min (d) 40 min
24. 24.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) 56 min (c) 2 min (d) 22 min
25. 25.What is the smallest number of sweets that can be shared equally among 16 children or among 28 children, with none left over? (a) 224 (b) 44 (c) 112 (d) 448
26. 26.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) 10 (b) 30 (c) 5 (d) 40
27. 27.What is the smallest number of sweets that can be shared equally among 6 children or among 14 children, with none left over? (a) 84 (b) 42 (c) 20 (d) 43
28. 28.Two ribbons are 18 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) 27 cm (b) 18 cm (c) 9 cm (d) 3 cm
29. 29.A teacher has 20 pencils and 45 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 20 (b) 1 (c) 5 (d) 25
30. 30.Two ribbons are 14 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) 7 cm (b) 1 cm (c) 42 cm (d) 14 cm
31. 31.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) 5 min (b) 45 min (c) 100 min (d) 500 min
32. 32.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) 6 cm (b) 30 cm (c) 3 cm (d) 18 cm
33. 33.What is the smallest number of sweets that can be shared equally among 12 children or among 20 children, with none left over? (a) 120 (b) 32 (c) 60 (d) 240
34. 34.Two ribbons are 40 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) 40 cm (b) 32 cm (c) 8 cm (d) 4 cm
35. 35.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) 26 min (b) 84 min (c) 2 min (d) 168 min
36. 36.A teacher has 36 pencils and 84 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 36 (c) 12 (d) 48
37. 37.What is the smallest number of sweets that can be shared equally among 25 children or among 30 children, with none left over? (a) 750 (b) 150 (c) 55 (d) 300
38. 38.A teacher has 20 pencils and 32 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 12 (b) 4 (c) 20 (d) 2
39. 39.Two bells ring every 18 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 126 min (b) 3 min (c) 39 min (d) 378 min
40. 40.Two bells ring every 15 minutes and every 18 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 270 min (b) 3 min (c) 33 min (d) 90 min

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