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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 438 · 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 420 cm long and 360 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  2. 2.A hall floor is 280 cm long and 80 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 5, 20 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.Three temple bells ring every 5, 9 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.Three temple bells ring every 15, 20 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.Three temple bells ring every 15, 5 and 10 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 9 that leaves a remainder of 4 when divided by 9, 6 or 8.
  8. 8.Three temple bells ring every 6, 18 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.Farhan takes 50 seconds and Diya takes 75 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.Tara takes 40 seconds and Aditya 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?
  11. 11.A hall floor is 150 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  12. 12.Karan takes 54 seconds and Meera 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?
  13. 13.Dev takes 50 seconds and Diya 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?
  14. 14.A hall floor is 100 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  15. 15.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 3, 6 or 10.
  16. 16.A hall floor is 175 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  17. 17.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?
  18. 18.Two tanks hold 360 litres and 405 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  19. 19.Two tanks hold 50 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  20. 20.Nisha takes 45 seconds and Rohan 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?
  21. 21.Aarav takes 40 seconds and Pooja 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?
  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.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 15, 5 or 12.
  24. 24.A hall floor is 320 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  25. 25.Three temple bells ring every 20, 15 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Two tanks hold 210 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  27. 27.Ananya takes 80 seconds and Rohan 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?
  28. 28.Three temple bells ring every 30, 8 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Vivaan takes 72 seconds and Ishaan 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?
  30. 30.Diya takes 48 seconds and Isha 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?
  31. 31.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 8, 3 or 12.
  32. 32.Three temple bells ring every 5, 8 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.A hall floor is 400 cm long and 250 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  34. 34.A hall floor is 400 cm long and 350 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  35. 35.Two tanks hold 25 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  36. 36.Meera takes 60 seconds and Dev 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?
  37. 37.Meera takes 30 seconds and Diya 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?
  38. 38.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 4, 8 or 5.
  39. 39.A hall floor is 90 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  40. 40.Rahul takes 72 seconds and Rohan 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?

Answer key

  1. 42
  2. 14
  3. 60
  4. 90
  5. 60
  6. 30
  7. 76
  8. 90
  9. 150
  10. 200
  11. 6
  12. 432
  13. 400
  14. 10
  15. 32
  16. 21
  17. 12
  18. 45
  19. 10
  20. 180
  21. 360
  22. 90
  23. 63
  24. 40
  25. 60
  26. 30
  27. 240
  28. 120
  29. 360
  30. 144
  31. 25
  32. 120
  33. 40
  34. 56
  35. 5
  36. 540
  37. 150
  38. 41
  39. 6
  40. 144

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