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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 135 · 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.Pooja takes 30 seconds and Rohan 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?
  2. 2.Three temple bells ring every 30, 5 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.A hall floor is 90 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  4. 4.Priya takes 50 seconds and Diya 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?
  5. 5.Kavya takes 80 seconds and Zoya 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?
  6. 6.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 9, 12 or 5.
  7. 7.A hall floor is 135 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  8. 8.Two tanks hold 450 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  9. 9.A hall floor is 160 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  10. 10.A hall floor is 350 cm long and 300 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  11. 11.Three temple bells ring every 15, 8 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 3, 8 or 5.
  13. 13.Three temple bells ring every 24, 4 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.Two tanks hold 405 litres and 360 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  15. 15.Three temple bells ring every 8, 6 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.Three temple bells ring every 10, 12 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.Rohan takes 60 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?
  18. 18.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?
  19. 19.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?
  20. 20.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 8, 4 or 5.
  21. 21.A hall floor is 240 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  22. 22.A hall floor is 200 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  23. 23.Kabir takes 40 seconds and Pooja 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?
  24. 24.Three temple bells ring every 20, 30 and 12 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 9 that leaves a remainder of 2 when divided by 9, 4 or 3.
  26. 26.Three temple bells ring every 6, 5 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.Priya takes 90 seconds and Rohan 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?
  28. 28.Rohan takes 45 seconds and Sneha takes 75 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.Two tanks hold 15 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  30. 30.Three temple bells ring every 24, 10 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.Three temple bells ring every 8, 24 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.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?
  33. 33.Three temple bells ring every 9, 6 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.Two tanks hold 10 litres and 25 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  35. 35.Two tanks hold 15 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  36. 36.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 10, 3 or 12.
  37. 37.Three temple bells ring every 18, 5 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.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?
  39. 39.Three temple bells ring every 24, 30 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  40. 40.Three temple bells ring every 24, 8 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 240
  2. 60
  3. 6
  4. 300
  5. 240
  6. 183
  7. 6
  8. 50
  9. 12
  10. 42
  11. 120
  12. 121
  13. 120
  14. 45
  15. 72
  16. 60
  17. 180
  18. 14
  19. 14
  20. 42
  21. 24
  22. 24
  23. 360
  24. 60
  25. 38
  26. 90
  27. 360
  28. 225
  29. 5
  30. 120
  31. 120
  32. 21
  33. 90
  34. 5
  35. 5
  36. 61
  37. 90
  38. 10
  39. 120
  40. 120

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