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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 500 · 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.Two tanks hold 200 litres and 350 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  2. 2.Two tanks hold 200 litres and 250 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  3. 3.A hall floor is 210 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  4. 4.Sneha takes 60 seconds and Aarav 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?
  5. 5.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 6, 4 or 15.
  6. 6.Three temple bells ring every 6, 12 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.Find the smallest number bigger than 6 that leaves a remainder of 2 when divided by 4, 6 or 3.
  8. 8.Three temple bells ring every 10, 6 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.Three temple bells ring every 4, 15 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.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?
  11. 11.Three temple bells ring every 6, 18 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.Two tanks hold 120 litres and 210 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  13. 13.Two tanks hold 80 litres and 360 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.Two tanks hold 75 litres and 135 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  15. 15.A hall floor is 280 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 4, 18 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.Two tanks hold 140 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  18. 18.Three temple bells ring every 8, 12 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Two tanks hold 120 litres and 320 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  20. 20.Two tanks hold 270 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  21. 21.Rahul takes 90 seconds and Zoya takes 50 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?
  22. 22.Three temple bells ring every 10, 15 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.Meera takes 75 seconds and Karan 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?
  24. 24.Isha takes 30 seconds and Aarav 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?
  25. 25.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 5, 3 or 6.
  26. 26.Three temple bells ring every 24, 8 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.Three temple bells ring every 15, 5 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.Find the smallest number bigger than 12 that leaves a remainder of 4 when divided by 12, 9 or 6.
  29. 29.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 5, 3 or 10.
  30. 30.A hall floor is 125 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  31. 31.Three temple bells ring every 30, 10 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 6, 15 or 4.
  33. 33.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 4, 8 or 3.
  34. 34.Two tanks hold 10 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  35. 35.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 10, 8 or 15.
  36. 36.Two tanks hold 50 litres and 125 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  37. 37.Pooja takes 30 seconds and Priya 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?
  38. 38.Two tanks hold 150 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  39. 39.A hall floor is 200 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  40. 40.Three temple bells ring every 30, 8 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 50
  2. 50
  3. 28
  4. 240
  5. 62
  6. 36
  7. 14
  8. 90
  9. 60
  10. 10
  11. 36
  12. 30
  13. 40
  14. 15
  15. 14
  16. 72
  17. 20
  18. 72
  19. 40
  20. 30
  21. 450
  22. 60
  23. 600
  24. 240
  25. 31
  26. 120
  27. 30
  28. 40
  29. 32
  30. 10
  31. 120
  32. 62
  33. 26
  34. 5
  35. 121
  36. 25
  37. 120
  38. 30
  39. 15
  40. 120

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