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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 393 · 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 280 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  2. 2.Three temple bells ring every 10, 12 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.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?
  4. 4.Two tanks hold 80 litres and 60 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 4, 15 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.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?
  7. 7.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 8, 12 or 10.
  8. 8.Three temple bells ring every 18, 5 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.Isha takes 36 seconds and Dev 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?
  10. 10.Two tanks hold 80 litres and 280 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  11. 11.Three temple bells ring every 15, 5 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.A hall floor is 350 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  13. 13.Two tanks hold 200 litres and 125 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 140 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  15. 15.Three temple bells ring every 9, 24 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.Find the smallest number bigger than 5 that leaves a remainder of 2 when divided by 3, 5 or 4.
  17. 17.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 8, 6 or 3.
  18. 18.Three temple bells ring every 24, 8 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 15, 12 or 8.
  20. 20.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 8, 5 or 12.
  21. 21.Three temple bells ring every 4, 9 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.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?
  23. 23.A hall floor is 100 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  24. 24.Three temple bells ring every 15, 5 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 3 or 10.
  26. 26.Sneha takes 45 seconds and Saanvi 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?
  27. 27.Two tanks hold 25 litres and 35 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 8, 30 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.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?
  30. 30.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 5 or 6.
  31. 31.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 4 or 12.
  32. 32.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?
  33. 33.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?
  34. 34.Arjun takes 36 seconds and Karan 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?
  35. 35.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 4, 9 or 6.
  36. 36.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?
  37. 37.Two tanks hold 25 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  38. 38.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 3, 15 or 9.
  39. 39.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?
  40. 40.Two tanks hold 315 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?

Answer key

  1. 40
  2. 60
  3. 60
  4. 20
  5. 120
  6. 120
  7. 122
  8. 90
  9. 180
  10. 40
  11. 30
  12. 28
  13. 25
  14. 21
  15. 72
  16. 62
  17. 25
  18. 120
  19. 123
  20. 123
  21. 36
  22. 6
  23. 10
  24. 120
  25. 62
  26. 90
  27. 5
  28. 120
  29. 50
  30. 32
  31. 61
  32. 30
  33. 28
  34. 360
  35. 38
  36. 14
  37. 5
  38. 46
  39. 35
  40. 45

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