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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 167 · 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 30 litres and 20 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 80 litres and 120 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 8, 20 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 6, 3 or 10.
  5. 5.Rohan takes 36 seconds and Pooja 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?
  6. 6.A hall floor is 315 cm long and 225 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  7. 7.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 4, 5 or 12.
  8. 8.Kabir takes 54 seconds and Arjun 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?
  9. 9.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?
  10. 10.Three temple bells ring every 9, 18 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.Two tanks hold 50 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  12. 12.Two tanks hold 20 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  13. 13.Dev takes 36 seconds and Meera 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?
  14. 14.A hall floor is 160 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  15. 15.Dev takes 36 seconds and Farhan 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?
  16. 16.Two tanks hold 75 litres and 135 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  17. 17.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 3, 4 or 8.
  18. 18.Two tanks hold 45 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  19. 19.Two tanks hold 180 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  20. 20.Two tanks hold 20 litres and 15 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  21. 21.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 3 or 9.
  22. 22.Three temple bells ring every 15, 6 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.Two tanks hold 20 litres and 35 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  24. 24.Two tanks hold 100 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  25. 25.Three temple bells ring every 30, 4 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.A hall floor is 160 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  27. 27.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 10, 3 or 15.
  28. 28.Three temple bells ring every 9, 10 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 8, 4 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.Three temple bells ring every 4, 10 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.Three temple bells ring every 6, 30 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.Aditya takes 60 seconds and Pooja 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?
  33. 33.Two tanks hold 180 litres and 405 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 100 litres and 75 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 6, 20 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.Three temple bells ring every 30, 4 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  37. 37.Two tanks hold 320 litres and 120 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 3 when divided by 10, 4 or 15.
  39. 39.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 8 or 5.
  40. 40.Three temple bells ring every 24, 5 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 10
  2. 40
  3. 40
  4. 31
  5. 720
  6. 35
  7. 61
  8. 108
  9. 21
  10. 90
  11. 10
  12. 10
  13. 180
  14. 12
  15. 144
  16. 15
  17. 25
  18. 5
  19. 45
  20. 5
  21. 37
  22. 30
  23. 5
  24. 20
  25. 60
  26. 24
  27. 31
  28. 90
  29. 40
  30. 120
  31. 90
  32. 180
  33. 45
  34. 25
  35. 60
  36. 60
  37. 40
  38. 63
  39. 121
  40. 120

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