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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 144 · 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.Find the smallest number bigger than 6 that leaves a remainder of 2 when divided by 3, 4 or 6.
  2. 2.Two tanks hold 75 litres and 125 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  3. 3.Zoya takes 75 seconds and Sneha 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?
  4. 4.A hall floor is 315 cm long and 135 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  5. 5.Three temple bells ring every 4, 8 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.Three temple bells ring every 9, 24 and 8 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, 4 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.Two tanks hold 280 litres and 80 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 480 cm long and 300 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  10. 10.Aditya takes 40 seconds and Ananya 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?
  11. 11.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?
  12. 12.Three temple bells ring every 30, 6 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.Find the smallest number bigger than 15 that leaves a remainder of 6 when divided by 15, 12 or 10.
  14. 14.Arjun takes 36 seconds and Ishaan 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?
  15. 15.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 10, 15 or 8.
  16. 16.Three temple bells ring every 10, 8 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.Two tanks hold 320 litres and 360 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  18. 18.A hall floor is 175 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  19. 19.Three temple bells ring every 9, 30 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.Three temple bells ring every 15, 6 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.Three temple bells ring every 4, 12 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Three temple bells ring every 15, 5 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 4, 6 or 15.
  24. 24.Two tanks hold 75 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  25. 25.Three temple bells ring every 30, 5 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Two tanks hold 350 litres and 450 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  27. 27.Three temple bells ring every 5, 12 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.Three temple bells ring every 10, 30 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 9, 15 or 12.
  30. 30.Three temple bells ring every 5, 10 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.Two tanks hold 50 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  32. 32.A hall floor is 120 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  33. 33.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?
  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.A hall floor is 160 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  36. 36.Three temple bells ring every 6, 15 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  37. 37.Two tanks hold 180 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  38. 38.A hall floor is 300 cm long and 250 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  39. 39.Two tanks hold 90 litres and 210 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  40. 40.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 4, 3 or 8.

Answer key

  1. 14
  2. 25
  3. 600
  4. 21
  5. 24
  6. 72
  7. 24
  8. 40
  9. 40
  10. 240
  11. 42
  12. 60
  13. 66
  14. 180
  15. 121
  16. 40
  17. 40
  18. 42
  19. 90
  20. 120
  21. 60
  22. 120
  23. 63
  24. 15
  25. 60
  26. 50
  27. 60
  28. 60
  29. 184
  30. 40
  31. 10
  32. 12
  33. 50
  34. 25
  35. 40
  36. 90
  37. 20
  38. 30
  39. 30
  40. 26

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