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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 296 · 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.Three temple bells ring every 20, 6 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.Three temple bells ring every 8, 30 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.Farhan takes 72 seconds and Pooja 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?
  4. 4.Pooja takes 45 seconds and Meera 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?
  5. 5.A hall floor is 120 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  6. 6.A hall floor is 160 cm long and 140 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  7. 7.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?
  8. 8.Three temple bells ring every 6, 10 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.Rohan takes 80 seconds and Tara 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?
  10. 10.A hall floor is 210 cm long and 180 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 5, 9 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.Two tanks hold 20 litres and 30 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 60 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 6, 3 or 15.
  15. 15.Rahul takes 36 seconds and Isha takes 45 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?
  16. 16.Two tanks hold 80 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  17. 17.Two tanks hold 45 litres and 25 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 24, 5 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Two tanks hold 60 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  20. 20.Find the smallest number bigger than 9 that leaves a remainder of 3 when divided by 8, 4 or 9.
  21. 21.Three temple bells ring every 6, 5 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  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.Three temple bells ring every 4, 6 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Three temple bells ring every 6, 9 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.Three temple bells ring every 10, 12 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.A hall floor is 140 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  27. 27.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?
  28. 28.Three temple bells ring every 20, 30 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Two tanks hold 160 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  30. 30.Two tanks hold 250 litres and 400 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  31. 31.Manav takes 50 seconds and Ishaan 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?
  32. 32.Three temple bells ring every 15, 10 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.Three temple bells ring every 30, 9 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.Isha takes 72 seconds and Pooja takes 45 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?
  35. 35.A hall floor is 240 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  36. 36.Rahul takes 72 seconds and Aditya 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?
  37. 37.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?
  38. 38.Dev takes 40 seconds and Rahul 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?
  39. 39.A hall floor is 180 cm long and 135 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  40. 40.Sneha takes 60 seconds and Pooja 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?

Answer key

  1. 60
  2. 120
  3. 144
  4. 180
  5. 30
  6. 56
  7. 60
  8. 60
  9. 240
  10. 42
  11. 45
  12. 10
  13. 15
  14. 32
  15. 180
  16. 20
  17. 5
  18. 120
  19. 20
  20. 75
  21. 60
  22. 60
  23. 60
  24. 36
  25. 60
  26. 21
  27. 35
  28. 120
  29. 20
  30. 50
  31. 150
  32. 90
  33. 90
  34. 360
  35. 12
  36. 720
  37. 72
  38. 360
  39. 12
  40. 300

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