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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 23 · 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 450 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  2. 2.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 4, 6 or 15.
  3. 3.Three temple bells ring every 9, 12 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.Two tanks hold 50 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  5. 5.Three temple bells ring every 18, 30 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.A hall floor is 315 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  7. 7.A hall floor is 150 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  8. 8.Two tanks hold 160 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  9. 9.Two tanks hold 180 litres and 315 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 350 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  11. 11.Isha takes 60 seconds and Ishaan 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?
  12. 12.Three temple bells ring every 6, 4 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.Three temple bells ring every 5, 20 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.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?
  15. 15.Two tanks hold 10 litres and 25 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  16. 16.Three temple bells ring every 8, 4 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.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?
  18. 18.Three temple bells ring every 9, 8 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Three temple bells ring every 9, 18 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 3, 10 or 5.
  21. 21.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 3, 12 or 15.
  22. 22.A hall floor is 225 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  23. 23.Dev takes 45 seconds and Nisha 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?
  24. 24.Three temple bells ring every 6, 9 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.Two tanks hold 150 litres and 100 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 18, 30 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 4, 6 or 12.
  28. 28.A hall floor is 200 cm long and 175 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  29. 29.Two tanks hold 280 litres and 320 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 18, 4 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.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?
  32. 32.Three temple bells ring every 24, 10 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.Two tanks hold 105 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  34. 34.Two tanks hold 450 litres and 400 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  35. 35.Three temple bells ring every 8, 6 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.Three temple bells ring every 24, 4 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  37. 37.A hall floor is 140 cm long and 60 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 8 that leaves a remainder of 1 when divided by 3, 8 or 6.
  39. 39.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?
  40. 40.Pooja takes 45 seconds and Isha 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?

Answer key

  1. 50
  2. 63
  3. 72
  4. 10
  5. 90
  6. 14
  7. 6
  8. 20
  9. 45
  10. 14
  11. 180
  12. 60
  13. 40
  14. 50
  15. 5
  16. 72
  17. 40
  18. 72
  19. 36
  20. 32
  21. 61
  22. 10
  23. 180
  24. 72
  25. 50
  26. 90
  27. 15
  28. 56
  29. 40
  30. 72
  31. 30
  32. 120
  33. 15
  34. 50
  35. 24
  36. 120
  37. 21
  38. 25
  39. 21
  40. 360

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