HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 806 · 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) 504 (b) 168 (c) 54 (d) 84
2. 2.Two ribbons are 15 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) 12 cm (b) 3 cm (c) 15 cm (d) 1 cm
3. 3.What is the smallest number of sweets that can be shared equally among 10 children or among 25 children, with none left over? (a) 100 (b) 50 (c) 35 (d) 250
4. 4.Two ribbons are 12 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) 1 cm (c) 12 cm (d) 84 cm
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) 3 min (b) 252 min (c) 84 min (d) 33 min
6. 6.What is the smallest number of sweets that can be shared equally among 12 children or among 14 children, with none left over? (a) 168 (b) 85 (c) 26 (d) 84
7. 7.A teacher has 15 pencils and 27 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 12 (c) 15 (d) 1
8. 8.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) 6 (b) 252 (c) 3 (d) 36
9. 9.What is the smallest number of sweets that can be shared equally among 6 children or among 8 children, with none left over? (a) 24 (b) 14 (c) 25 (d) 48
10. 10.What is the smallest number of sweets that can be shared equally among 20 children or among 28 children, with none left over? (a) 48 (b) 560 (c) 280 (d) 140
11. 11.Two bells ring every 15 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 3 min (b) 36 min (c) 315 min (d) 105 min
12. 12.Two ribbons are 21 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) 1 cm (b) 14 cm (c) 7 cm (d) 21 cm
13. 13.Two bells ring every 12 minutes and every 15 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 3 min (b) 60 min (c) 180 min (d) 27 min
14. 14.Two ribbons are 4 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) 4 cm (b) 6 cm (c) 1 cm (d) 2 cm
15. 15.A teacher has 12 pencils and 16 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 4 (b) 48 (c) 2 (d) 12
16. 16.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) 448 min (b) 4 min (c) 112 min (d) 44 min
17. 17.A teacher has 9 pencils and 15 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 9 (c) 1 (d) 3
18. 18.Two bells ring every 10 minutes and every 12 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 22 min (b) 120 min (c) 60 min (d) 2 min
19. 19.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) 360 (d) 120
20. 20.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) 3 (b) 36 (c) 180 (d) 9
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) 375 min (b) 75 min (c) 5 min (d) 40 min
22. 22.A teacher has 32 pencils and 40 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 8 (b) 32 (c) 4 (d) 160
23. 23.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) 42 min (b) 84 min (c) 20 min (d) 2 min
24. 24.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) 35 min (b) 5 min (c) 250 min (d) 50 min
25. 25.What is the smallest number of sweets that can be shared equally among 10 children or among 35 children, with none left over? (a) 140 (b) 45 (c) 70 (d) 350
26. 26.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) 2 (c) 10 (d) 1
27. 27.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) 15 min (c) 18 min (d) 54 min
28. 28.Two ribbons are 22 cm and 33 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) 22 cm (d) 66 cm
29. 29.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) 6 cm (b) 24 cm (c) 12 cm (d) 36 cm
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) 42 cm (b) 1 cm (c) 7 cm (d) 14 cm
31. 31.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) 150 min (b) 25 min (c) 5 min (d) 30 min
32. 32.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) 2 (b) 16 (c) 12 (d) 4
33. 33.A teacher has 21 pencils and 35 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 21 (b) 7 (c) 14 (d) 1
34. 34.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) 60 cm (b) 360 cm (c) 6 cm (d) 12 cm
35. 35.Two ribbons are 8 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) 8 cm (b) 2 cm (c) 10 cm (d) 1 cm
36. 36.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) 1 (b) 28 (c) 35 (d) 7
37. 37.What is the smallest number of sweets that can be shared equally among 6 children or among 15 children, with none left over? (a) 60 (b) 21 (c) 90 (d) 30
38. 38.A teacher has 16 pencils and 40 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 24 (b) 4 (c) 16 (d) 8
39. 39.A teacher has 30 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) 10 (c) 40 (d) 30
40. 40.What is the smallest number of sweets that can be shared equally among 16 children or among 28 children, with none left over? (a) 448 (b) 112 (c) 224 (d) 44

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