HCF and LCM Worksheet for Maths Olympiad

Maths Olympiad topic 8: HCF and LCM puzzles · Set 554 · 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 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) 9 (b) 15 (c) 3 (d) 1
2. 2.Two ribbons are 32 cm and 40 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) 160 cm (c) 4 cm (d) 8 cm
3. 3.A teacher has 14 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) 14 (c) 7 (d) 42
4. 4.A teacher has 18 pencils and 48 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 18 (b) 3 (c) 6 (d) 30
5. 5.Two ribbons are 4 cm and 10 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) 1 cm (c) 4 cm (d) 6 cm
6. 6.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) 40 min (c) 4 min (d) 28 min
7. 7.A teacher has 49 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) 7 (d) 1
8. 8.What is the smallest number of sweets that can be shared equally among 8 children or among 28 children, with none left over? (a) 224 (b) 112 (c) 36 (d) 56
9. 9.Two ribbons are 40 cm and 50 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) 5 cm (c) 200 cm (d) 40 cm
10. 10.What is the smallest number of sweets that can be shared equally among 10 children or among 15 children, with none left over? (a) 30 (b) 150 (c) 25 (d) 60
11. 11.A teacher has 44 pencils and 77 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 33 (c) 44 (d) 11
12. 12.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) 48 min (c) 540 min (d) 90 min
13. 13.What is the smallest number of sweets that can be shared equally among 8 children or among 14 children, with none left over? (a) 112 (b) 22 (c) 57 (d) 56
14. 14.Two ribbons are 18 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) 18 cm (b) 126 cm (c) 3 cm (d) 1 cm
15. 15.What is the smallest number of sweets that can be shared equally among 10 children or among 35 children, with none left over? (a) 140 (b) 350 (c) 45 (d) 70
16. 16.Two ribbons are 33 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) 33 cm (b) 55 cm (c) 11 cm (d) 1 cm
17. 17.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) 3 min (b) 270 min (c) 33 min (d) 90 min
18. 18.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) 2 min (b) 60 min (c) 16 min (d) 30 min
19. 19.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) 42 min (b) 432 min (c) 6 min (d) 72 min
20. 20.Two ribbons are 12 cm and 15 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) 60 cm (c) 1 cm (d) 3 cm
21. 21.A teacher has 20 pencils and 25 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 100 (b) 1 (c) 5 (d) 20
22. 22.Two ribbons are 21 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) 1 cm (b) 35 cm (c) 21 cm (d) 7 cm
23. 23.A teacher has 55 pencils and 66 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 55 (b) 330 (c) 11 (d) 1
24. 24.A teacher has 63 pencils and 72 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 63 (b) 9 (c) 3 (d) 504
25. 25.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) 55 min (b) 5 min (c) 150 min (d) 750 min
26. 26.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) 126 min (b) 27 min (c) 3 min (d) 42 min
27. 27.Two ribbons are 56 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) 4 cm (b) 16 cm (c) 56 cm (d) 8 cm
28. 28.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) 720 (c) 10 (d) 80
29. 29.A teacher has 16 pencils and 28 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 16 (b) 2 (c) 4 (d) 12
30. 30.A teacher has 54 pencils and 63 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 3 (b) 54 (c) 9 (d) 378
31. 31.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) 375 min (b) 5 min (c) 40 min (d) 75 min
32. 32.Two bells ring every 6 minutes and every 15 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 30 min (b) 3 min (c) 21 min (d) 90 min
33. 33.A teacher has 20 pencils and 70 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 50 (b) 5 (c) 20 (d) 10
34. 34.Two ribbons are 30 cm and 50 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) 30 cm (d) 10 cm
35. 35.Two ribbons are 20 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) 10 cm (b) 5 cm (c) 70 cm (d) 20 cm
36. 36.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) 12 cm (b) 18 cm (c) 3 cm (d) 6 cm
37. 37.Two ribbons are 50 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) 300 cm (b) 5 cm (c) 50 cm (d) 10 cm
38. 38.Two ribbons are 20 cm and 50 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) 5 cm (c) 10 cm (d) 20 cm
39. 39.Two ribbons are 6 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) 1 cm (b) 2 cm (c) 10 cm (d) 6 cm
40. 40.A teacher has 12 pencils and 32 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 20 (b) 2 (c) 4 (d) 12

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