HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 550 · 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 4 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 28 min (b) 56 min (c) 2 min (d) 18 min
2. 2.A teacher has 48 pencils and 108 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 60 (b) 48 (c) 12 (d) 6
3. 3.What is the smallest number of sweets that can be shared equally among 6 children or among 15 children, with none left over? (a) 90 (b) 21 (c) 60 (d) 30
4. 4.What is the smallest number of sweets that can be shared equally among 15 children or among 35 children, with none left over? (a) 105 (b) 525 (c) 210 (d) 50
5. 5.A teacher has 42 pencils and 48 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 42 (b) 6 (c) 336 (d) 3
6. 6.Two ribbons are 32 cm and 56 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) 24 cm (c) 32 cm (d) 4 cm
7. 7.A teacher has 27 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) 9 (c) 27 (d) 18
8. 8.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) 28 min (b) 192 min (c) 48 min (d) 4 min
9. 9.A teacher has 25 pencils and 40 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 15 (b) 1 (c) 25 (d) 5
10. 10.What is the smallest number of sweets that can be shared equally among 4 children or among 14 children, with none left over? (a) 28 (b) 29 (c) 56 (d) 18
11. 11.A teacher has 28 pencils and 35 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 28 (b) 7 (c) 1 (d) 140
12. 12.What is the smallest number of sweets that can be shared equally among 9 children or among 12 children, with none left over? (a) 36 (b) 21 (c) 72 (d) 108
13. 13.A teacher has 10 pencils and 16 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 6 (c) 2 (d) 10
14. 14.A teacher has 24 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) 24 (c) 168 (d) 4
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) 24 (c) 25 (d) 48
16. 16.What is the smallest number of sweets that can be shared equally among 20 children or among 25 children, with none left over? (a) 100 (b) 500 (c) 200 (d) 45
17. 17.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) 2 (b) 20 (c) 12 (d) 4
18. 18.Two ribbons are 9 cm and 12 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) 9 cm (c) 36 cm (d) 1 cm
19. 19.Two ribbons are 16 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) 2 cm (b) 4 cm (c) 16 cm (d) 20 cm
20. 20.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) 2 cm (b) 8 cm (c) 28 cm (d) 4 cm
21. 21.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) 120 (c) 240 (d) 480
22. 22.Two ribbons are 6 cm and 9 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) 1 cm (c) 6 cm (d) 18 cm
23. 23.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) 60 min (c) 240 min (d) 4 min
24. 24.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
25. 25.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) 160 min (c) 4 min (d) 40 min
26. 26.A teacher has 45 pencils and 72 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 9 (b) 27 (c) 45 (d) 3
27. 27.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) 120 (c) 35 (d) 300
28. 28.What is the smallest number of sweets that can be shared equally among 9 children or among 21 children, with none left over? (a) 30 (b) 126 (c) 63 (d) 189
29. 29.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) 126 min (c) 42 min (d) 27 min
30. 30.A teacher has 16 pencils and 56 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 40 (b) 4 (c) 16 (d) 8
31. 31.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) 240 (c) 60 (d) 32
32. 32.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) 2 min (d) 60 min
33. 33.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) 60 min (b) 30 min (c) 16 min (d) 2 min
34. 34.Two ribbons are 12 cm and 32 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 20 cm (b) 12 cm (c) 2 cm (d) 4 cm
35. 35.Two ribbons are 30 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) 3 cm (c) 6 cm (d) 12 cm
36. 36.Two ribbons are 36 cm and 63 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) 36 cm (c) 3 cm (d) 9 cm
37. 37.A teacher has 21 pencils and 56 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 35 (b) 21 (c) 7 (d) 1
38. 38.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) 6 (b) 12 (c) 36 (d) 24
39. 39.Two bells ring every 20 minutes and every 28 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 140 min (b) 560 min (c) 48 min (d) 4 min
40. 40.A teacher has 80 pencils and 90 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 5 (b) 80 (c) 10 (d) 720

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