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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 211 · 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 75 litres and 120 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 360 litres and 160 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 70 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  4. 4.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?
  5. 5.Three temple bells ring every 4, 10 and 15 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, 24 and 10 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 9 that leaves a remainder of 3 when divided by 6, 8 or 9.
  8. 8.Kavya takes 80 seconds and Ananya 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?
  9. 9.Meera takes 48 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.Three temple bells ring every 4, 12 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 3, 10 or 5.
  12. 12.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 10 or 4.
  13. 13.A hall floor is 250 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  14. 14.Two tanks hold 90 litres and 20 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 45 litres and 10 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  16. 16.Two tanks hold 360 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  17. 17.Three temple bells ring every 12, 5 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.Meera takes 45 seconds and Farhan 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?
  19. 19.Two tanks hold 360 litres and 135 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  20. 20.A hall floor is 200 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  21. 21.Three temple bells ring every 12, 30 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Two tanks hold 175 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  23. 23.Two tanks hold 210 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  24. 24.Aarav takes 30 seconds and Rahul 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?
  25. 25.Three temple bells ring every 24, 6 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Two tanks hold 50 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  27. 27.Three temple bells ring every 18, 24 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.A hall floor is 300 cm long and 250 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  29. 29.Tara takes 36 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?
  30. 30.Rahul takes 45 seconds and Priya 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?
  31. 31.Arjun takes 30 seconds and Aarav takes 75 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?
  32. 32.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?
  33. 33.A hall floor is 175 cm long and 125 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  34. 34.Two tanks hold 280 litres and 160 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  35. 35.Kabir takes 72 seconds and Nisha 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?
  36. 36.Three temple bells ring every 10, 8 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  37. 37.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 8, 5 or 10.
  38. 38.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?
  39. 39.A hall floor is 140 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  40. 40.Three temple bells ring every 4, 18 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 15
  2. 40
  3. 10
  4. 40
  5. 60
  6. 120
  7. 75
  8. 720
  9. 720
  10. 60
  11. 32
  12. 61
  13. 20
  14. 10
  15. 5
  16. 40
  17. 60
  18. 90
  19. 45
  20. 24
  21. 120
  22. 25
  23. 30
  24. 240
  25. 120
  26. 25
  27. 72
  28. 30
  29. 180
  30. 720
  31. 150
  32. 30
  33. 35
  34. 40
  35. 720
  36. 40
  37. 43
  38. 45
  39. 14
  40. 36

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