HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 553 · 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 14 children, with none left over? (a) 168 (b) 26 (c) 84 (d) 85
2. 2.A teacher has 6 pencils and 15 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 9 (b) 1 (c) 3 (d) 6
3. 3.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) 60 cm (c) 24 cm (d) 12 cm
4. 4.Two ribbons are 66 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) 66 cm (c) 462 cm (d) 11 cm
5. 5.Two ribbons are 12 cm and 30 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 18 cm (b) 6 cm (c) 3 cm (d) 12 cm
6. 6.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) 6 min (b) 54 min (c) 120 min (d) 720 min
7. 7.A teacher has 21 pencils and 24 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 21 (b) 1 (c) 3 (d) 168
8. 8.Two bells ring every 6 minutes and every 8 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 24 min (b) 48 min (c) 2 min (d) 14 min
9. 9.A teacher has 64 pencils and 72 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 4 (b) 576 (c) 8 (d) 64
10. 10.A teacher has 60 pencils and 84 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 24 (b) 6 (c) 12 (d) 60
11. 11.What is the smallest number of sweets that can be shared equally among 8 children or among 20 children, with none left over? (a) 28 (b) 40 (c) 160 (d) 80
12. 12.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) 7 cm (c) 1 cm (d) 14 cm
13. 13.What is the smallest number of sweets that can be shared equally among 8 children or among 12 children, with none left over? (a) 24 (b) 48 (c) 96 (d) 20
14. 14.What is the smallest number of sweets that can be shared equally among 10 children or among 15 children, with none left over? (a) 150 (b) 60 (c) 25 (d) 30
15. 15.What is the smallest number of sweets that can be shared equally among 6 children or among 8 children, with none left over? (a) 14 (b) 25 (c) 24 (d) 48
16. 16.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) 84 min (b) 168 min (c) 26 min (d) 2 min
17. 17.Two bells ring every 12 minutes and every 16 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 4 min (b) 28 min (c) 48 min (d) 192 min
18. 18.Two ribbons are 15 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) 20 cm (c) 5 cm (d) 15 cm
19. 19.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) 10 cm (b) 1 cm (c) 4 cm (d) 2 cm
20. 20.What is the smallest number of sweets that can be shared equally among 15 children or among 20 children, with none left over? (a) 60 (b) 300 (c) 35 (d) 120
21. 21.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) 10 cm (b) 8 cm (c) 2 cm (d) 1 cm
22. 22.Two ribbons are 18 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) 6 cm (b) 18 cm (c) 24 cm (d) 3 cm
23. 23.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) 160 (c) 320 (d) 36
24. 24.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) 9 cm (b) 18 cm (c) 27 cm (d) 3 cm
25. 25.A teacher has 21 pencils and 49 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 21 (b) 28 (c) 1 (d) 7
26. 26.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) 27 min (c) 180 min (d) 60 min
27. 27.Two bells ring every 4 minutes and every 6 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 2 min (b) 10 min (c) 12 min (d) 24 min
28. 28.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) 6 min (b) 432 min (c) 72 min (d) 42 min
29. 29.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) 5 min (d) 25 min
30. 30.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) 90 min (b) 270 min (c) 3 min (d) 33 min
31. 31.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) 360 min (b) 6 min (c) 42 min (d) 60 min
32. 32.What is the smallest number of sweets that can be shared equally among 10 children or among 14 children, with none left over? (a) 24 (b) 71 (c) 70 (d) 140
33. 33.Two ribbons are 32 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) 32 cm (b) 2 cm (c) 288 cm (d) 4 cm
34. 34.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) 30 (d) 90
35. 35.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) 42 (c) 84 (d) 43
36. 36.Two ribbons are 12 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) 36 cm (b) 6 cm (c) 12 cm (d) 3 cm
37. 37.A teacher has 15 pencils and 40 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 15 (c) 5 (d) 25
38. 38.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) 50 min (b) 105 min (c) 525 min (d) 5 min
39. 39.A teacher has 48 pencils and 54 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 432 (b) 3 (c) 6 (d) 48
40. 40.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

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