HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 431 · 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 ribbons are 40 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) 40 cm (b) 5 cm (c) 30 cm (d) 10 cm
2. 2.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) 8 (b) 24 (c) 16 (d) 4
3. 3.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) 5 (c) 10 (d) 25
4. 4.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) 50 min (b) 5 min (c) 250 min (d) 35 min
5. 5.A teacher has 70 pencils and 80 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 560 (b) 5 (c) 10 (d) 70
6. 6.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) 45 (d) 200
7. 7.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) 60 (c) 15 (d) 1
8. 8.A teacher has 84 pencils and 96 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 84 (c) 12 (d) 672
9. 9.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) 36 cm (b) 24 cm (c) 12 cm (d) 6 cm
10. 10.Two ribbons are 49 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) 7 cm (b) 49 cm (c) 392 cm (d) 1 cm
11. 11.Two ribbons are 54 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) 3 cm (b) 9 cm (c) 378 cm (d) 54 cm
12. 12.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) 15 cm (b) 1 cm (c) 3 cm (d) 6 cm
13. 13.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) 36 (c) 3 (d) 252
14. 14.Two ribbons are 4 cm and 6 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) 1 cm (d) 12 cm
15. 15.Two ribbons are 28 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) 28 cm (c) 140 cm (d) 7 cm
16. 16.Two ribbons are 45 cm and 54 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 45 cm (b) 270 cm (c) 3 cm (d) 9 cm
17. 17.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) 6 cm (b) 240 cm (c) 48 cm (d) 12 cm
18. 18.A teacher has 12 pencils and 27 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 12 (c) 3 (d) 15
19. 19.Two ribbons are 64 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) 64 cm (b) 4 cm (c) 8 cm (d) 576 cm
20. 20.Two ribbons are 28 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) 7 cm (b) 35 cm (c) 28 cm (d) 1 cm
21. 21.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) 160 min (b) 4 min (c) 40 min (d) 28 min
22. 22.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) 6 (b) 3 (c) 24 (d) 30
23. 23.A teacher has 12 pencils and 18 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 36 (c) 12 (d) 3
24. 24.Two ribbons are 33 cm and 55 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) 33 cm (c) 22 cm (d) 11 cm
25. 25.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) 10 cm (b) 2 cm (c) 6 cm (d) 1 cm
26. 26.Two ribbons are 24 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) 24 cm (b) 4 cm (c) 8 cm (d) 32 cm
27. 27.What is the smallest number of sweets that can be shared equally among 18 children or among 21 children, with none left over? (a) 378 (b) 126 (c) 252 (d) 39
28. 28.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) 160 (c) 4 (d) 32
29. 29.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) 54 min (b) 18 min (c) 15 min (d) 3 min
30. 30.A teacher has 24 pencils and 36 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 72 (c) 12 (d) 24
31. 31.What is the smallest number of sweets that can be shared equally among 6 children or among 21 children, with none left over? (a) 126 (b) 27 (c) 84 (d) 42
32. 32.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) 4 min (b) 112 min (c) 448 min (d) 44 min
33. 33.What is the smallest number of sweets that can be shared equally among 12 children or among 42 children, with none left over? (a) 54 (b) 168 (c) 84 (d) 504
34. 34.Two ribbons are 77 cm and 88 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 616 cm (b) 11 cm (c) 77 cm (d) 1 cm
35. 35.A teacher has 40 pencils and 72 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) 40
36. 36.A teacher has 8 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) 40 (c) 8 (d) 2
37. 37.Two bells ring every 20 minutes and every 25 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 45 min (b) 100 min (c) 500 min (d) 5 min
38. 38.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) 7 cm (c) 21 cm (d) 14 cm
39. 39.A teacher has 16 pencils and 36 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 20 (b) 4 (c) 16 (d) 2
40. 40.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) 12 min (b) 10 min (c) 2 min (d) 24 min

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