HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 196 · 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 12 minutes and every 28 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 336 min (b) 4 min (c) 40 min (d) 84 min
2. 2.Two bells ring every 12 minutes and every 30 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 42 min (b) 6 min (c) 60 min (d) 360 min
3. 3.Two ribbons are 24 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) 36 cm (b) 24 cm (c) 6 cm (d) 12 cm
4. 4.What is the smallest number of sweets that can be shared equally among 10 children or among 25 children, with none left over? (a) 50 (b) 100 (c) 35 (d) 250
5. 5.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) 84 min (b) 33 min (c) 3 min (d) 252 min
6. 6.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) 3 min (b) 27 min (c) 126 min (d) 42 min
7. 7.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) 4 min (c) 20 min (d) 24 min
8. 8.What is the smallest number of sweets that can be shared equally among 16 children or among 20 children, with none left over? (a) 320 (b) 36 (c) 80 (d) 160
9. 9.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) 70 min (b) 45 min (c) 5 min (d) 350 min
10. 10.Two ribbons are 33 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) 1 cm (c) 44 cm (d) 33 cm
11. 11.A teacher has 77 pencils and 88 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 77 (b) 616 (c) 1 (d) 11
12. 12.Two ribbons are 60 cm and 70 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) 420 cm (c) 5 cm (d) 10 cm
13. 13.A teacher has 50 pencils and 60 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 300 (b) 50 (c) 10 (d) 5
14. 14.Two ribbons are 45 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) 45 cm (c) 9 cm (d) 270 cm
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) 72 (b) 108 (c) 36 (d) 21
16. 16.A teacher has 88 pencils and 99 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 11 (b) 88 (c) 792 (d) 1
17. 17.Two bells ring every 6 minutes and every 10 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 16 min (b) 60 min (c) 2 min (d) 30 min
18. 18.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) 5 min (b) 35 min (c) 250 min (d) 50 min
19. 19.A teacher has 60 pencils and 108 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 48 (c) 60 (d) 12
20. 20.A teacher has 35 pencils and 49 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 7 (c) 14 (d) 35
21. 21.A teacher has 20 pencils and 90 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 10 (b) 5 (c) 20 (d) 70
22. 22.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) 2 cm (b) 40 cm (c) 8 cm (d) 1 cm
23. 23.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) 36 min (b) 224 min (c) 4 min (d) 56 min
24. 24.A teacher has 36 pencils and 42 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 36 (b) 6 (c) 3 (d) 252
25. 25.What is the smallest number of sweets that can be shared equally among 25 children or among 30 children, with none left over? (a) 150 (b) 55 (c) 300 (d) 750
26. 26.What is the smallest number of sweets that can be shared equally among 8 children or among 12 children, with none left over? (a) 48 (b) 24 (c) 96 (d) 20
27. 27.What is the smallest number of sweets that can be shared equally among 12 children or among 30 children, with none left over? (a) 42 (b) 60 (c) 120 (d) 360
28. 28.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
29. 29.What is the smallest number of sweets that can be shared equally among 20 children or among 25 children, with none left over? (a) 500 (b) 45 (c) 200 (d) 100
30. 30.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) 3 min (b) 54 min (c) 15 min (d) 18 min
31. 31.What is the smallest number of sweets that can be shared equally among 10 children or among 12 children, with none left over? (a) 120 (b) 61 (c) 60 (d) 22
32. 32.What is the smallest number of sweets that can be shared equally among 20 children or among 24 children, with none left over? (a) 44 (b) 480 (c) 120 (d) 240
33. 33.Two ribbons are 12 cm and 42 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) 12 cm (c) 3 cm (d) 6 cm
34. 34.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) 75 min (c) 375 min (d) 40 min
35. 35.A teacher has 10 pencils and 35 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 25 (b) 5 (c) 1 (d) 10
36. 36.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) 16 (c) 31 (d) 30
37. 37.What is the smallest number of sweets that can be shared equally among 8 children or among 20 children, with none left over? (a) 160 (b) 28 (c) 80 (d) 40
38. 38.A teacher has 30 pencils and 48 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 30 (b) 18 (c) 6 (d) 3
39. 39.What is the smallest number of sweets that can be shared equally among 10 children or among 15 children, with none left over? (a) 25 (b) 150 (c) 30 (d) 60
40. 40.A teacher has 16 pencils and 24 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 8 (b) 48 (c) 4 (d) 16

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