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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 455 · 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 45 litres and 75 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 25 litres and 15 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  3. 3.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 10, 6 or 4.
  4. 4.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?
  5. 5.Three temple bells ring every 8, 5 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.Isha takes 60 seconds and Karan 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?
  7. 7.Three temple bells ring every 10, 6 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.A hall floor is 350 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  9. 9.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?
  10. 10.A hall floor is 150 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 8, 10 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.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?
  13. 13.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 4 or 10.
  14. 14.Three temple bells ring every 5, 24 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  15. 15.Three temple bells ring every 5, 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 4, 20 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 3, 9 or 15.
  18. 18.Three temple bells ring every 8, 10 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Two tanks hold 90 litres and 405 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  20. 20.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?
  21. 21.Farhan takes 72 seconds and Dev 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?
  22. 22.Rahul takes 54 seconds and Ananya takes 72 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?
  23. 23.Two tanks hold 150 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  24. 24.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 3, 10 or 8.
  25. 25.Kabir takes 90 seconds and Zoya takes 80 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?
  26. 26.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 10, 9 or 4.
  27. 27.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?
  28. 28.A hall floor is 180 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  29. 29.Vivaan takes 80 seconds and Arjun 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?
  30. 30.Three temple bells ring every 6, 12 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 12, 3 or 15.
  32. 32.Priya takes 60 seconds and Farhan 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?
  33. 33.Two tanks hold 40 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  34. 34.A hall floor is 150 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  35. 35.A hall floor is 350 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  36. 36.Meera 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?
  37. 37.Three temple bells ring every 4, 12 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.A hall floor is 60 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  39. 39.A hall floor is 240 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  40. 40.Two tanks hold 405 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?

Answer key

  1. 15
  2. 5
  3. 61
  4. 5
  5. 120
  6. 240
  7. 60
  8. 21
  9. 15
  10. 15
  11. 120
  12. 30
  13. 61
  14. 120
  15. 90
  16. 40
  17. 47
  18. 120
  19. 45
  20. 72
  21. 360
  22. 216
  23. 30
  24. 121
  25. 720
  26. 182
  27. 40
  28. 30
  29. 240
  30. 24
  31. 62
  32. 300
  33. 5
  34. 10
  35. 28
  36. 180
  37. 60
  38. 6
  39. 40
  40. 45

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