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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 457 · 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.Two tanks hold 405 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  2. 2.Two tanks hold 120 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  3. 3.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?
  4. 4.Meera takes 54 seconds and Aditya 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?
  5. 5.Pooja takes 72 seconds and Aditya 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?
  6. 6.A hall floor is 240 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  7. 7.Arjun takes 36 seconds and Rahul 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?
  8. 8.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 12, 5 or 9.
  9. 9.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?
  10. 10.Three temple bells ring every 12, 10 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.A hall floor is 175 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  12. 12.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?
  13. 13.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?
  14. 14.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?
  15. 15.Dev takes 48 seconds and Manav 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?
  16. 16.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?
  17. 17.Two tanks hold 180 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  18. 18.Find the smallest number bigger than 9 that leaves a remainder of 3 when divided by 9, 4 or 6.
  19. 19.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 10, 6 or 4.
  20. 20.Three temple bells ring every 5, 10 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.Karan takes 30 seconds and Ananya 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?
  22. 22.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 3, 4 or 15.
  23. 23.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 8 or 4.
  24. 24.Two tanks hold 30 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  25. 25.Karan takes 48 seconds and Diya 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.Two tanks hold 30 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  27. 27.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 3, 15 or 8.
  28. 28.Three temple bells ring every 12, 8 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Three temple bells ring every 24, 30 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.A hall floor is 300 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  31. 31.Two tanks hold 25 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  32. 32.Three temple bells ring every 8, 6 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.Farhan takes 40 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?
  34. 34.Isha takes 50 seconds and Arjun 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?
  35. 35.Three temple bells ring every 5, 6 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 6 or 4.
  37. 37.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 4, 6 or 3.
  38. 38.Find the smallest number bigger than 12 that leaves a remainder of 4 when divided by 10, 9 or 12.
  39. 39.Dev takes 50 seconds and Isha 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?
  40. 40.A hall floor is 180 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?

Answer key

  1. 45
  2. 30
  3. 50
  4. 270
  5. 216
  6. 24
  7. 180
  8. 183
  9. 72
  10. 60
  11. 42
  12. 6
  13. 40
  14. 6
  15. 144
  16. 24
  17. 20
  18. 39
  19. 61
  20. 90
  21. 270
  22. 61
  23. 121
  24. 10
  25. 720
  26. 10
  27. 122
  28. 120
  29. 120
  30. 15
  31. 5
  32. 120
  33. 240
  34. 150
  35. 60
  36. 14
  37. 13
  38. 184
  39. 450
  40. 6

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