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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 55 · 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).

NameDateTime takenScore ___ / 40
  1. 1.A hall floor is 480 cm long and 420 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  2. 2.Aditya takes 54 seconds and Arjun 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?
  3. 3.Two tanks hold 120 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.Three temple bells ring every 20, 5 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.A hall floor is 315 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  6. 6.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 3, 9 or 4.
  7. 7.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 4, 12 or 3.
  8. 8.Three temple bells ring every 8, 30 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.Three temple bells ring every 24, 18 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.Two tanks hold 50 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  11. 11.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?
  12. 12.Two tanks hold 20 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  13. 13.A hall floor is 140 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  14. 14.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 8, 5 or 12.
  15. 15.A hall floor is 120 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  16. 16.Three temple bells ring every 12, 10 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.A hall floor is 270 cm long and 225 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  18. 18.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 4, 8 or 5.
  19. 19.Three temple bells ring every 20, 6 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.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?
  21. 21.Three temple bells ring every 8, 6 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.A hall floor is 360 cm long and 135 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  23. 23.A hall floor is 80 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  24. 24.Farhan takes 45 seconds and Arjun takes 40 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?
  25. 25.Three temple bells ring every 4, 12 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.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?
  27. 27.Two tanks hold 40 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  28. 28.Three temple bells ring every 30, 5 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Ishaan takes 80 seconds and Arjun 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?
  30. 30.Three temple bells ring every 10, 18 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.Two tanks hold 240 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  32. 32.Two tanks hold 250 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  33. 33.Three temple bells ring every 4, 8 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.Two tanks hold 100 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  35. 35.Three temple bells ring every 8, 9 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.A hall floor is 250 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  37. 37.Find the smallest number bigger than 12 that leaves a remainder of 4 when divided by 12, 10 or 9.
  38. 38.Ishaan takes 48 seconds and Meera takes 40 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.Three temple bells ring every 5, 24 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  40. 40.Two tanks hold 225 litres and 405 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?

Answer key

  1. 56
  2. 432
  3. 30
  4. 60
  5. 28
  6. 37
  7. 14
  8. 120
  9. 72
  10. 10
  11. 15
  12. 10
  13. 21
  14. 121
  15. 6
  16. 60
  17. 30
  18. 41
  19. 60
  20. 14
  21. 120
  22. 24
  23. 12
  24. 360
  25. 60
  26. 21
  27. 20
  28. 120
  29. 720
  30. 90
  31. 30
  32. 50
  33. 72
  34. 25
  35. 72
  36. 10
  37. 184
  38. 240
  39. 120
  40. 45

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