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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 115 · 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 175 cm long and 75 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 8 that leaves a remainder of 1 when divided by 5, 8 or 6.
  3. 3.Three temple bells ring every 4, 8 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.Two tanks hold 280 litres and 240 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  5. 5.Rahul takes 40 seconds and Manav 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?
  6. 6.A hall floor is 315 cm long and 135 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  7. 7.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?
  8. 8.Three temple bells ring every 4, 6 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.Two tanks hold 35 litres and 15 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  10. 10.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?
  11. 11.Ishaan takes 75 seconds and Aarav 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?
  12. 12.Two tanks hold 30 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  13. 13.Three temple bells ring every 5, 15 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.Rahul takes 40 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?
  15. 15.Two tanks hold 90 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  16. 16.A hall floor is 480 cm long and 300 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  17. 17.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 6 or 10.
  18. 18.Two tanks hold 45 litres and 105 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  19. 19.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?
  20. 20.Three temple bells ring every 4, 9 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.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?
  22. 22.Two tanks hold 240 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  23. 23.Rahul takes 48 seconds and Diya 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?
  24. 24.Three temple bells ring every 10, 5 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.Three temple bells ring every 6, 30 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Three temple bells ring every 10, 4 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.Three temple bells ring every 10, 18 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.Find the smallest number bigger than 6 that leaves a remainder of 3 when divided by 5, 6 or 4.
  29. 29.Kavya takes 48 seconds and Farhan 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?
  30. 30.Three temple bells ring every 6, 8 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 6, 8 or 15.
  32. 32.Three temple bells ring every 4, 5 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.Two tanks hold 270 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  34. 34.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?
  35. 35.Two tanks hold 35 litres and 25 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  36. 36.Two tanks hold 160 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  37. 37.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 6, 8 or 15.
  38. 38.Rohan takes 90 seconds and Kavya 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?
  39. 39.A hall floor is 175 cm long and 125 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  40. 40.Dev takes 72 seconds and Nisha 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?

Answer key

  1. 21
  2. 121
  3. 40
  4. 40
  5. 360
  6. 21
  7. 15
  8. 24
  9. 5
  10. 40
  11. 150
  12. 15
  13. 120
  14. 360
  15. 10
  16. 40
  17. 31
  18. 15
  19. 20
  20. 72
  21. 6
  22. 30
  23. 240
  24. 90
  25. 60
  26. 60
  27. 90
  28. 63
  29. 240
  30. 24
  31. 123
  32. 60
  33. 45
  34. 14
  35. 5
  36. 40
  37. 121
  38. 720
  39. 35
  40. 360

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