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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 433 · 40 questions
TalentJR

The method (LCM or HCF?): Bells, lights, runners “together again”: find the LCM of the gaps. Biggest can, rope piece or tile that fits exactly: find the HCF. Leaves the same remainder r every time: LCM + r. Number of tiles = (length ÷ tile side) × (width ÷ tile side).

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  1. 1.Two tanks hold 60 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  2. 2.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 4, 5 or 6.
  3. 3.Two tanks hold 120 litres and 280 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  4. 4.Three temple bells ring every 9, 8 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.Two tanks hold 360 litres and 135 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  6. 6.Three temple bells ring every 30, 24 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.Three temple bells ring every 8, 15 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.Two tanks hold 225 litres and 360 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  9. 9.Arjun takes 60 seconds and Manav takes 72 seconds to run once round a track. They start together from the start line. After how many seconds will they first be at the start line together again?
  10. 10.A hall floor is 280 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  11. 11.A hall floor is 175 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  12. 12.Kavya takes 30 seconds and Arjun takes 45 seconds to run once round a track. They start together from the start line. After how many seconds will they first be at the start line together again?
  13. 13.Three temple bells ring every 9, 4 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.A hall floor is 480 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  15. 15.Pooja takes 45 seconds and Ishaan takes 30 seconds to run once round a track. They start together from the start line. After how many seconds will they first be at the start line together again?
  16. 16.Two tanks hold 30 litres and 135 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  17. 17.Three temple bells ring every 8, 24 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 4, 5 or 9.
  19. 19.A hall floor is 350 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  20. 20.Two tanks hold 140 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  21. 21.Two tanks hold 90 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  22. 22.A hall floor is 225 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  23. 23.Two tanks hold 150 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  24. 24.Three temple bells ring every 6, 18 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.Two tanks hold 40 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  26. 26.Three temple bells ring every 4, 5 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.Rohan takes 30 seconds and Tara takes 45 seconds to run once round a track. They start together from the start line. After how many seconds will they first be at the start line together again?
  28. 28.A hall floor is 100 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  29. 29.A hall floor is 200 cm long and 175 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  30. 30.Two tanks hold 120 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  31. 31.Two tanks hold 180 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  32. 32.Three temple bells ring every 24, 5 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.A hall floor is 250 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  34. 34.Zoya takes 60 seconds and Diya takes 90 seconds to run once round a track. They start together from the start line. After how many seconds will they first be at the start line together again?
  35. 35.Two tanks hold 45 litres and 35 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  36. 36.Three temple bells ring every 12, 30 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  37. 37.Two tanks hold 25 litres and 10 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  38. 38.Three temple bells ring every 9, 24 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.Three temple bells ring every 10, 24 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  40. 40.A hall floor is 360 cm long and 300 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?

Answer key

  1. 10
  2. 61
  3. 40
  4. 72
  5. 45
  6. 120
  7. 120
  8. 45
  9. 360
  10. 21
  11. 14
  12. 90
  13. 36
  14. 24
  15. 90
  16. 15
  17. 120
  18. 181
  19. 28
  20. 20
  21. 10
  22. 10
  23. 30
  24. 36
  25. 10
  26. 60
  27. 90
  28. 15
  29. 56
  30. 30
  31. 20
  32. 120
  33. 15
  34. 180
  35. 5
  36. 60
  37. 5
  38. 72
  39. 120
  40. 30

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