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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 542 · 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 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?
  2. 2.A hall floor is 480 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  3. 3.Three temple bells ring every 6, 18 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.A hall floor is 160 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  5. 5.A hall floor is 420 cm long and 300 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  6. 6.Two tanks hold 75 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  7. 7.Three temple bells ring every 6, 8 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.Two tanks hold 105 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  9. 9.Three temple bells ring every 12, 6 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.Three temple bells ring every 5, 6 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.Three temple bells ring every 12, 6 and 20 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 15 that leaves a remainder of 4 when divided by 9, 15 or 12.
  13. 13.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 10, 3 or 5.
  14. 14.Three temple bells ring every 15, 10 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  15. 15.Find the smallest number bigger than 6 that leaves a remainder of 3 when divided by 6, 5 or 4.
  16. 16.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 8, 3 or 4.
  17. 17.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 6, 8 or 4.
  18. 18.Three temple bells ring every 4, 5 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.A hall floor is 150 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  20. 20.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?
  21. 21.Rohan takes 45 seconds and Pooja 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?
  22. 22.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 12 or 3.
  23. 23.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 5, 15 or 8.
  24. 24.Sneha takes 30 seconds and Priya 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?
  25. 25.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 10, 12 or 3.
  26. 26.Zoya takes 72 seconds and Nisha 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?
  27. 27.Manav takes 30 seconds and Sneha 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?
  28. 28.Three temple bells ring every 4, 15 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Three temple bells ring every 10, 4 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.A hall floor is 250 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  31. 31.Rahul takes 45 seconds and Aarav 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?
  32. 32.Tara takes 45 seconds and Kabir 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?
  33. 33.Three temple bells ring every 4, 5 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.Two tanks hold 45 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  35. 35.Arjun takes 40 seconds and Aarav 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?
  36. 36.Aarav takes 45 seconds and Farhan 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?
  37. 37.Two tanks hold 100 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  38. 38.Kavya takes 36 seconds and Tara 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?
  39. 39.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 4, 3 or 15.
  40. 40.Three temple bells ring every 5, 10 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 40
  2. 24
  3. 36
  4. 24
  5. 35
  6. 15
  7. 120
  8. 15
  9. 60
  10. 60
  11. 60
  12. 184
  13. 32
  14. 60
  15. 63
  16. 26
  17. 25
  18. 60
  19. 20
  20. 120
  21. 720
  22. 61
  23. 124
  24. 240
  25. 61
  26. 360
  27. 240
  28. 60
  29. 60
  30. 10
  31. 270
  32. 720
  33. 120
  34. 15
  35. 360
  36. 720
  37. 20
  38. 180
  39. 61
  40. 90

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