HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 530 · 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 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) 64 (d) 8
2. 2.Two ribbons are 10 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) 6 cm (b) 1 cm (c) 2 cm (d) 10 cm
3. 3.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) 6 (b) 60 (c) 12 (d) 24
4. 4.A teacher has 18 pencils and 30 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 18 (c) 3 (d) 12
5. 5.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) 4 min (b) 240 min (c) 60 min (d) 32 min
6. 6.A teacher has 20 pencils and 24 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 2 (b) 4 (c) 20 (d) 120
7. 7.What is the smallest number of sweets that can be shared equally among 6 children or among 8 children, with none left over? (a) 48 (b) 25 (c) 14 (d) 24
8. 8.Two ribbons are 15 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) 3 cm (b) 6 cm (c) 1 cm (d) 15 cm
9. 9.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) 24 min (b) 2 min (c) 10 min (d) 12 min
10. 10.A teacher has 21 pencils and 28 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 7 (b) 21 (c) 84 (d) 1
11. 11.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) 4 (b) 32 (c) 160 (d) 8
12. 12.What is the smallest number of sweets that can be shared equally among 8 children or among 28 children, with none left over? (a) 36 (b) 224 (c) 56 (d) 112
13. 13.A teacher has 6 pencils and 10 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) 4 (d) 2
14. 14.What is the smallest number of sweets that can be shared equally among 16 children or among 28 children, with none left over? (a) 112 (b) 44 (c) 224 (d) 448
15. 15.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) 2 min (b) 56 min (c) 112 min (d) 22 min
16. 16.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) 15 min (b) 3 min (c) 18 min (d) 54 min
17. 17.Two ribbons are 18 cm and 81 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) 63 cm (d) 3 cm
18. 18.What is the smallest number of sweets that can be shared equally among 4 children or among 6 children, with none left over? (a) 10 (b) 24 (c) 13 (d) 12
19. 19.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) 10 cm (b) 60 cm (c) 5 cm (d) 420 cm
20. 20.Two ribbons are 60 cm and 108 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) 12 cm (c) 48 cm (d) 6 cm
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) 75 min (b) 375 min (c) 40 min (d) 5 min
22. 22.What is the smallest number of sweets that can be shared equally among 4 children or among 10 children, with none left over? (a) 21 (b) 14 (c) 20 (d) 40
23. 23.Two ribbons are 10 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) 1 cm (d) 2 cm
24. 24.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) 27 min (d) 180 min
25. 25.Two bells ring every 20 minutes and every 35 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 5 min (b) 140 min (c) 55 min (d) 700 min
26. 26.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) 2 min (b) 18 min (c) 56 min (d) 28 min
27. 27.What is the smallest number of sweets that can be shared equally among 12 children or among 18 children, with none left over? (a) 36 (b) 72 (c) 30 (d) 216
28. 28.Two ribbons are 24 cm and 28 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) 24 cm (c) 2 cm (d) 168 cm
29. 29.Two ribbons are 35 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) 21 cm (b) 1 cm (c) 35 cm (d) 7 cm
30. 30.Two ribbons are 8 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) 4 cm (b) 2 cm (c) 24 cm (d) 8 cm
31. 31.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) 1 (b) 9 (c) 3 (d) 12
32. 32.Two ribbons are 18 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) 9 cm (b) 3 cm (c) 18 cm (d) 45 cm
33. 33.What is the smallest number of sweets that can be shared equally among 8 children or among 20 children, with none left over? (a) 40 (b) 28 (c) 80 (d) 160
34. 34.Two ribbons are 24 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) 72 cm (b) 6 cm (c) 12 cm (d) 24 cm
35. 35.What is the smallest number of sweets that can be shared equally among 20 children or among 24 children, with none left over? (a) 120 (b) 480 (c) 44 (d) 240
36. 36.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) 36 (c) 160 (d) 320
37. 37.A teacher has 15 pencils and 20 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 5 (b) 1 (c) 60 (d) 15
38. 38.Two bells ring every 10 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 70 min (b) 140 min (c) 2 min (d) 24 min
39. 39.What is the smallest number of sweets that can be shared equally among 6 children or among 9 children, with none left over? (a) 36 (b) 15 (c) 18 (d) 54
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) 10 (c) 80 (d) 720

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