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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 218 · 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.A hall floor is 180 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  2. 2.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?
  3. 3.Two tanks hold 30 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  4. 4.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 10 or 3.
  5. 5.Three temple bells ring every 6, 20 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.A hall floor is 210 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  7. 7.Three temple bells ring every 30, 4 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.Two tanks hold 200 litres and 280 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  9. 9.Three temple bells ring every 8, 5 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.Three temple bells ring every 8, 12 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.Three temple bells ring every 4, 18 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.Three temple bells ring every 30, 24 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.Rohan takes 50 seconds and Aditya 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?
  14. 14.Two tanks hold 60 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  15. 15.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 6, 3 or 10.
  16. 16.Two tanks hold 70 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  17. 17.Two tanks hold 120 litres and 140 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  18. 18.Find the smallest number bigger than 15 that leaves a remainder of 7 when divided by 8, 10 or 15.
  19. 19.Two tanks hold 280 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  20. 20.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 10, 9 or 6.
  21. 21.Three temple bells ring every 10, 4 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.A hall floor is 210 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  23. 23.Three temple bells ring every 4, 10 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Three temple bells ring every 12, 20 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 8 or 12.
  26. 26.Rohan takes 80 seconds and Aditya 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?
  27. 27.A hall floor is 225 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  28. 28.Three temple bells ring every 10, 6 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Pooja takes 36 seconds and Arjun 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?
  30. 30.Two tanks hold 160 litres and 100 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 160 litres and 120 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 160 litres and 360 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 6, 8 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.Three temple bells ring every 9, 6 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.A hall floor is 125 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  36. 36.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 5 or 4.
  37. 37.Three temple bells ring every 8, 4 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.Find the smallest number bigger than 10 that leaves a remainder of 4 when divided by 8, 10 or 5.
  39. 39.A hall floor is 180 cm long and 135 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  40. 40.Aarav takes 36 seconds and Rohan 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?

Answer key

  1. 6
  2. 10
  3. 10
  4. 31
  5. 60
  6. 21
  7. 120
  8. 40
  9. 120
  10. 120
  11. 36
  12. 120
  13. 150
  14. 20
  15. 32
  16. 10
  17. 20
  18. 127
  19. 40
  20. 91
  21. 120
  22. 14
  23. 60
  24. 120
  25. 122
  26. 720
  27. 20
  28. 60
  29. 180
  30. 20
  31. 40
  32. 40
  33. 120
  34. 72
  35. 20
  36. 61
  37. 72
  38. 44
  39. 12
  40. 180

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