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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 277 · 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 210 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  2. 2.Two tanks hold 200 litres and 450 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  3. 3.Three temple bells ring every 30, 5 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.Farhan takes 72 seconds and Arjun 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?
  5. 5.Rohan takes 45 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?
  6. 6.A hall floor is 350 cm long and 300 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  7. 7.Isha takes 90 seconds and Nisha 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?
  8. 8.A hall floor is 200 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  9. 9.Three temple bells ring every 8, 10 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.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?
  11. 11.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?
  12. 12.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 9, 5 or 10.
  13. 13.Two tanks hold 280 litres and 160 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.A hall floor is 280 cm long and 240 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  15. 15.A hall floor is 360 cm long and 225 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  16. 16.Arjun takes 60 seconds and Saanvi 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?
  17. 17.A hall floor is 400 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  18. 18.Two tanks hold 120 litres and 320 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  19. 19.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 4, 10 or 3.
  20. 20.Two tanks hold 90 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  21. 21.Manav takes 45 seconds and Isha 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?
  22. 22.A hall floor is 125 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  23. 23.Two tanks hold 135 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  24. 24.Three temple bells ring every 10, 15 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.Three temple bells ring every 20, 8 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Two tanks hold 90 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  27. 27.Two tanks hold 20 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.Three temple bells ring every 6, 12 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Two tanks hold 250 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  30. 30.Three temple bells ring every 10, 30 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.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?
  32. 32.Sneha takes 45 seconds and Rahul 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?
  33. 33.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?
  34. 34.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 3 or 10.
  35. 35.Three temple bells ring every 9, 6 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.A hall floor is 350 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  37. 37.Two tanks hold 90 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  38. 38.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?
  39. 39.Three temple bells ring every 10, 8 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  40. 40.Three temple bells ring every 8, 30 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 14
  2. 50
  3. 120
  4. 144
  5. 360
  6. 42
  7. 180
  8. 12
  9. 40
  10. 20
  11. 20
  12. 91
  13. 40
  14. 42
  15. 40
  16. 120
  17. 24
  18. 40
  19. 62
  20. 30
  21. 720
  22. 10
  23. 45
  24. 120
  25. 120
  26. 30
  27. 10
  28. 60
  29. 50
  30. 60
  31. 21
  32. 90
  33. 6
  34. 62
  35. 90
  36. 21
  37. 10
  38. 30
  39. 120
  40. 120

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