HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 574 · 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 18 children or among 24 children, with none left over? (a) 72 (b) 432 (c) 144 (d) 42
2. 2.A teacher has 25 pencils and 35 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 10 (c) 25 (d) 5
3. 3.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) 224 min (b) 4 min (c) 56 min (d) 36 min
4. 4.Two ribbons are 20 cm and 25 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) 1 cm (c) 100 cm (d) 5 cm
5. 5.A teacher has 14 pencils and 63 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 14 (b) 49 (c) 1 (d) 7
6. 6.What is the smallest number of sweets that can be shared equally among 6 children or among 14 children, with none left over? (a) 42 (b) 43 (c) 84 (d) 20
7. 7.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) 12 cm (c) 6 cm (d) 3 cm
8. 8.Two ribbons are 36 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) 36 cm (c) 12 cm (d) 48 cm
9. 9.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) 2 cm (b) 288 cm (c) 32 cm (d) 4 cm
10. 10.Two bells ring every 25 minutes and every 30 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 750 min (b) 150 min (c) 5 min (d) 55 min
11. 11.Two ribbons are 70 cm and 90 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) 5 cm (c) 70 cm (d) 10 cm
12. 12.Two ribbons are 10 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) 5 cm (b) 10 cm (c) 1 cm (d) 25 cm
13. 13.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) 6 min (b) 540 min (c) 48 min (d) 90 min
14. 14.What is the smallest number of sweets that can be shared equally among 9 children or among 21 children, with none left over? (a) 63 (b) 189 (c) 30 (d) 126
15. 15.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
16. 16.Two ribbons are 48 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) 12 cm (b) 240 cm (c) 6 cm (d) 48 cm
17. 17.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) 4 (b) 8 (c) 24 (d) 16
18. 18.What is the smallest number of sweets that can be shared equally among 12 children or among 16 children, with none left over? (a) 192 (b) 28 (c) 96 (d) 48
19. 19.A teacher has 12 pencils and 42 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 6 (c) 30 (d) 12
20. 20.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) 56 min (b) 22 min (c) 112 min (d) 2 min
21. 21.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) 27 min (b) 42 min (c) 126 min (d) 3 min
22. 22.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) 200 (c) 45 (d) 100
23. 23.Two ribbons are 18 cm and 24 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) 72 cm
24. 24.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) 30 min (b) 60 min (c) 2 min (d) 16 min
25. 25.What is the smallest number of sweets that can be shared equally among 8 children or among 12 children, with none left over? (a) 96 (b) 20 (c) 24 (d) 48
26. 26.A teacher has 25 pencils and 45 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 25 (c) 5 (d) 20
27. 27.A teacher has 44 pencils and 99 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 11 (c) 55 (d) 44
28. 28.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) 48 (d) 24
29. 29.Two bells ring every 9 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 63 min (b) 3 min (c) 189 min (d) 30 min
30. 30.A teacher has 4 pencils and 6 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 2 (b) 1 (c) 4 (d) 12
31. 31.A teacher has 15 pencils and 24 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) 9 (d) 3
32. 32.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) 140 min (b) 5 min (c) 55 min (d) 700 min
33. 33.A teacher has 30 pencils and 54 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 24 (b) 30 (c) 6 (d) 3
34. 34.Two ribbons are 72 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) 72 cm (b) 12 cm (c) 504 cm (d) 6 cm
35. 35.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) 48 (b) 12 (c) 6 (d) 60
36. 36.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) 18 min (d) 15 min
37. 37.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) 160 (b) 4 (c) 32 (d) 8
38. 38.A teacher has 50 pencils and 80 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) 50 (d) 30
39. 39.A teacher has 28 pencils and 36 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 4 (b) 8 (c) 28 (d) 2
40. 40.A teacher has 14 pencils and 35 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 14 (b) 7 (c) 21 (d) 1

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