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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 572 · 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 160 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  2. 2.A hall floor is 315 cm long and 225 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  3. 3.A hall floor is 420 cm long and 240 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  4. 4.Three temple bells ring every 6, 12 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.A hall floor is 100 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  6. 6.Two tanks hold 45 litres and 20 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 9, 10 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.Three temple bells ring every 12, 24 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.A hall floor is 150 cm long and 125 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  10. 10.Arjun takes 60 seconds and Karan 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?
  11. 11.Two tanks hold 75 litres and 175 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  12. 12.Three temple bells ring every 6, 10 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.Zoya takes 36 seconds and Kabir 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 270 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.Ananya takes 40 seconds and Dev 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?
  16. 16.Two tanks hold 315 litres and 405 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  17. 17.Three temple bells ring every 15, 10 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.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?
  19. 19.A hall floor is 200 cm long and 80 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 5, 18 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 4, 10 or 9.
  22. 22.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 3, 4 or 8.
  23. 23.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?
  24. 24.A hall floor is 125 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  25. 25.Two tanks hold 75 litres and 125 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  26. 26.Three temple bells ring every 5, 6 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.Two tanks hold 135 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  28. 28.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 4, 12 or 5.
  29. 29.Vivaan takes 48 seconds and Pooja 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?
  30. 30.A hall floor is 140 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  31. 31.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 10, 3 or 5.
  32. 32.Three temple bells ring every 30, 15 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.Three temple bells ring every 8, 12 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.Three temple bells ring every 24, 5 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.Three temple bells ring every 20, 6 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.A hall floor is 210 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  37. 37.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 5, 9 or 15.
  38. 38.A hall floor is 120 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  39. 39.Three temple bells ring every 15, 24 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  40. 40.A hall floor is 140 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?

Answer key

  1. 12
  2. 35
  3. 28
  4. 60
  5. 20
  6. 5
  7. 90
  8. 120
  9. 30
  10. 180
  11. 25
  12. 30
  13. 360
  14. 30
  15. 200
  16. 45
  17. 90
  18. 60
  19. 10
  20. 90
  21. 181
  22. 25
  23. 6
  24. 20
  25. 25
  26. 120
  27. 45
  28. 63
  29. 240
  30. 35
  31. 31
  32. 120
  33. 120
  34. 120
  35. 60
  36. 14
  37. 49
  38. 12
  39. 120
  40. 14

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