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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 179 · 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.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?
  2. 2.Find the smallest number bigger than 6 that leaves a remainder of 2 when divided by 5, 4 or 6.
  3. 3.Two tanks hold 150 litres and 270 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  4. 4.A hall floor is 420 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  5. 5.Two tanks hold 90 litres and 70 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  6. 6.Two tanks hold 25 litres and 35 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  7. 7.Sneha takes 90 seconds and Karan takes 48 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?
  8. 8.A hall floor is 420 cm long and 360 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  9. 9.Three temple bells ring every 5, 12 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.Three temple bells ring every 18, 30 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.Two tanks hold 20 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  12. 12.Two tanks hold 225 litres and 270 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  13. 13.Three temple bells ring every 4, 30 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.Three temple bells ring every 6, 8 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  15. 15.Find the smallest number bigger than 6 that leaves a remainder of 2 when divided by 6, 4 or 3.
  16. 16.Two tanks hold 135 litres and 315 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  17. 17.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 5, 8 or 4.
  18. 18.A hall floor is 100 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  19. 19.A hall floor is 100 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  20. 20.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?
  21. 21.Two tanks hold 135 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  22. 22.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 4 or 3.
  23. 23.A hall floor is 315 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  24. 24.Two tanks hold 210 litres and 270 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  25. 25.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?
  26. 26.A hall floor is 300 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  27. 27.Three temple bells ring every 12, 8 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.Priya takes 45 seconds and Aditya takes 60 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?
  29. 29.Three temple bells ring every 5, 18 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.Two tanks hold 15 litres and 35 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  31. 31.Three temple bells ring every 15, 6 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.Isha takes 60 seconds and Farhan takes 80 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?
  33. 33.Three temple bells ring every 5, 8 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.Three temple bells ring every 18, 12 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.Two tanks hold 160 litres and 180 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 6, 9 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  37. 37.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 4, 6 or 12.
  38. 38.Arjun takes 60 seconds and Sneha takes 80 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?
  39. 39.Ananya takes 50 seconds and Kabir takes 60 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?
  40. 40.A hall floor is 150 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?

Answer key

  1. 120
  2. 62
  3. 30
  4. 21
  5. 10
  6. 5
  7. 720
  8. 42
  9. 60
  10. 90
  11. 5
  12. 45
  13. 60
  14. 120
  15. 14
  16. 45
  17. 42
  18. 12
  19. 20
  20. 10
  21. 15
  22. 62
  23. 14
  24. 30
  25. 45
  26. 10
  27. 120
  28. 180
  29. 90
  30. 5
  31. 60
  32. 240
  33. 40
  34. 36
  35. 20
  36. 36
  37. 14
  38. 240
  39. 300
  40. 15

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