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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 528 · 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 35 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  2. 2.Three temple bells ring every 8, 4 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 9, 10 or 12.
  4. 4.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 10, 12 or 6.
  5. 5.Two tanks hold 200 litres and 320 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  6. 6.Three temple bells ring every 15, 5 and 20 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 15 that leaves a remainder of 2 when divided by 3, 15 or 9.
  8. 8.Two tanks hold 80 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.Sneha takes 72 seconds and Isha 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?
  10. 10.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?
  11. 11.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?
  12. 12.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 5, 10 or 3.
  13. 13.Two tanks hold 60 litres and 270 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.A hall floor is 420 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  15. 15.Three temple bells ring every 30, 12 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.Three temple bells ring every 24, 12 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.Three temple bells ring every 6, 20 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.Three temple bells ring every 8, 18 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.A hall floor is 400 cm long and 150 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 12 that leaves a remainder of 1 when divided by 4, 12 or 8.
  21. 21.Ananya takes 60 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?
  22. 22.Three temple bells ring every 9, 18 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.Three temple bells ring every 5, 30 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Two tanks hold 75 litres and 105 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 8, 15 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Aditya takes 30 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?
  27. 27.Three temple bells ring every 5, 6 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.Three temple bells ring every 15, 5 and 4 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 10 that leaves a remainder of 2 when divided by 10, 3 or 9.
  30. 30.Two tanks hold 360 litres and 135 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  31. 31.A hall floor is 280 cm long and 240 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  32. 32.Ananya takes 60 seconds and Tara takes 54 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?
  33. 33.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?
  34. 34.Three temple bells ring every 15, 20 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.Two tanks hold 30 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  36. 36.Three temple bells ring every 10, 12 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  37. 37.Meera takes 45 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?
  38. 38.Three temple bells ring every 4, 8 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.Two tanks hold 80 litres and 70 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  40. 40.Three temple bells ring every 20, 5 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 5
  2. 40
  3. 181
  4. 61
  5. 40
  6. 60
  7. 47
  8. 40
  9. 360
  10. 60
  11. 42
  12. 31
  13. 30
  14. 14
  15. 60
  16. 72
  17. 60
  18. 72
  19. 24
  20. 25
  21. 120
  22. 90
  23. 120
  24. 15
  25. 120
  26. 240
  27. 60
  28. 60
  29. 92
  30. 45
  31. 42
  32. 540
  33. 12
  34. 120
  35. 10
  36. 120
  37. 720
  38. 120
  39. 10
  40. 60

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