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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 338 · 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 60 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  2. 2.A hall floor is 175 cm long and 100 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, 15 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.Dev takes 30 seconds and Ishaan 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?
  5. 5.Three temple bells ring every 8, 4 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.Three temple bells ring every 12, 8 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.A hall floor is 360 cm long and 315 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  8. 8.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 5 or 6.
  9. 9.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?
  10. 10.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 4, 10 or 8.
  11. 11.Three temple bells ring every 24, 5 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.Two tanks hold 135 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  13. 13.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 3, 4 or 10.
  14. 14.Two tanks hold 60 litres and 140 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  15. 15.Three temple bells ring every 9, 4 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.A hall floor is 480 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  17. 17.Two tanks hold 90 litres and 405 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  18. 18.Arjun takes 50 seconds and Sneha 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?
  19. 19.Three temple bells ring every 10, 18 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.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?
  21. 21.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 8, 6 or 4.
  22. 22.Meera takes 50 seconds and Ishaan 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?
  23. 23.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 10 or 4.
  24. 24.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 12, 10 or 4.
  25. 25.Pooja takes 48 seconds and Arjun 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?
  26. 26.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 3, 6 or 12.
  27. 27.Saanvi takes 80 seconds and Priya 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?
  28. 28.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?
  29. 29.Three temple bells ring every 20, 15 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.A hall floor is 140 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  31. 31.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?
  32. 32.Two tanks hold 400 litres and 250 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  33. 33.Three temple bells ring every 20, 12 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.Three temple bells ring every 6, 8 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.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?
  36. 36.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 10, 12 or 5.
  37. 37.A hall floor is 240 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  38. 38.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 10, 5 or 4.
  39. 39.Two tanks hold 120 litres and 210 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  40. 40.Two tanks hold 135 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?

Answer key

  1. 10
  2. 28
  3. 30
  4. 180
  5. 120
  6. 24
  7. 56
  8. 61
  9. 42
  10. 41
  11. 120
  12. 45
  13. 62
  14. 20
  15. 36
  16. 24
  17. 45
  18. 400
  19. 90
  20. 20
  21. 25
  22. 150
  23. 61
  24. 63
  25. 432
  26. 14
  27. 720
  28. 25
  29. 60
  30. 28
  31. 35
  32. 50
  33. 60
  34. 120
  35. 60
  36. 63
  37. 30
  38. 21
  39. 30
  40. 15

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