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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 548 · 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.A hall floor is 270 cm long and 225 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  2. 2.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 4, 12 or 6.
  3. 3.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 8 or 4.
  4. 4.Vivaan takes 36 seconds and Zoya 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?
  5. 5.Two tanks hold 45 litres and 35 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  6. 6.Two tanks hold 100 litres and 250 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 8, 4 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.Diya takes 80 seconds and Priya 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?
  9. 9.Two tanks hold 40 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  10. 10.Three temple bells ring every 5, 12 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.Three temple bells ring every 15, 6 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.A hall floor is 360 cm long and 300 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  13. 13.Arjun takes 60 seconds and Dev 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?
  14. 14.Two tanks hold 200 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  15. 15.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 3, 15 or 10.
  16. 16.Three temple bells ring every 5, 12 and 24 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, 9 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.Three temple bells ring every 30, 9 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Diya takes 80 seconds and Tara 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?
  20. 20.A hall floor is 75 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  21. 21.A hall floor is 420 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  22. 22.A hall floor is 160 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  23. 23.Rahul takes 40 seconds and Rohan 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?
  24. 24.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 3 or 8.
  25. 25.Sneha takes 48 seconds and Ananya 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?
  26. 26.Three temple bells ring every 18, 10 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 3, 15 or 5.
  28. 28.Three temple bells ring every 12, 6 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Three temple bells ring every 18, 6 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.Three temple bells ring every 8, 18 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.Farhan takes 60 seconds and Isha 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?
  32. 32.Three temple bells ring every 4, 30 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.A hall floor is 300 cm long and 240 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 24, 8 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.Find the smallest number bigger than 9 that leaves a remainder of 5 when divided by 8, 9 or 6.
  36. 36.Vivaan takes 54 seconds and Isha 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.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 10 or 4.
  38. 38.Three temple bells ring every 5, 24 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.Nisha takes 60 seconds and Saanvi takes 36 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?
  40. 40.Three temple bells ring every 8, 24 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 30
  2. 13
  3. 26
  4. 180
  5. 5
  6. 50
  7. 24
  8. 400
  9. 20
  10. 120
  11. 60
  12. 30
  13. 120
  14. 40
  15. 31
  16. 120
  17. 90
  18. 90
  19. 240
  20. 6
  21. 21
  22. 40
  23. 360
  24. 25
  25. 720
  26. 90
  27. 16
  28. 36
  29. 72
  30. 72
  31. 180
  32. 120
  33. 20
  34. 120
  35. 77
  36. 270
  37. 62
  38. 120
  39. 180
  40. 72

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