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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 267 · 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 250 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.Three temple bells ring every 12, 9 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.Isha takes 75 seconds and Aditya 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?
  4. 4.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?
  5. 5.Two tanks hold 60 litres and 270 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  6. 6.Three temple bells ring every 18, 6 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.Three temple bells ring every 15, 12 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.Meera takes 50 seconds and Priya 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?
  9. 9.Two tanks hold 10 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  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.Rohan takes 54 seconds and Tara 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 15, 24 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.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?
  14. 14.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 8, 15 or 5.
  15. 15.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 6, 8 or 3.
  16. 16.Nisha 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?
  17. 17.A hall floor is 180 cm long and 120 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 5, 15 and 20 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 12 that leaves a remainder of 1 when divided by 8, 12 or 3.
  20. 20.A hall floor is 300 cm long and 180 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 12 that leaves a remainder of 2 when divided by 8, 3 or 12.
  22. 22.Two tanks hold 75 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  23. 23.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 4 or 8.
  24. 24.Find the smallest number bigger than 12 that leaves a remainder of 6 when divided by 12, 8 or 10.
  25. 25.Find the smallest number bigger than 10 that leaves a remainder of 5 when divided by 9, 10 or 6.
  26. 26.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?
  27. 27.Three temple bells ring every 4, 20 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 210 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  29. 29.Farhan takes 50 seconds and Ishaan 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?
  30. 30.A hall floor is 420 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  31. 31.Two tanks hold 180 litres and 135 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  32. 32.Pooja takes 45 seconds and Aditya takes 50 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 135 litres and 75 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 60 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  35. 35.A hall floor is 280 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  36. 36.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?
  37. 37.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 6, 9 or 4.
  38. 38.Two tanks hold 175 litres and 200 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 280 cm long and 240 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 6, 5 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 50
  2. 36
  3. 600
  4. 25
  5. 30
  6. 72
  7. 120
  8. 450
  9. 5
  10. 90
  11. 270
  12. 120
  13. 36
  14. 122
  15. 25
  16. 180
  17. 6
  18. 60
  19. 25
  20. 15
  21. 26
  22. 25
  23. 121
  24. 126
  25. 95
  26. 10
  27. 60
  28. 21
  29. 400
  30. 14
  31. 45
  32. 450
  33. 15
  34. 20
  35. 14
  36. 45
  37. 37
  38. 25
  39. 42
  40. 60

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