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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 38 · 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 315 litres and 360 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 24, 20 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.Kabir takes 90 seconds and Nisha 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?
  4. 4.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?
  5. 5.Three temple bells ring every 6, 10 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.A hall floor is 125 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  7. 7.A hall floor is 120 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  8. 8.A hall floor is 280 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  9. 9.Tara takes 90 seconds and Meera takes 54 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.Manav takes 40 seconds and Pooja 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?
  11. 11.A hall floor is 150 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  12. 12.Three temple bells ring every 8, 20 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.Two tanks hold 30 litres and 25 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.Nisha takes 60 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?
  15. 15.A hall floor is 175 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  16. 16.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 4, 9 or 12.
  17. 17.Rohan takes 50 seconds and Karan 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?
  18. 18.Three temple bells ring every 30, 12 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Three temple bells ring every 10, 15 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.Vivaan takes 30 seconds and Isha 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?
  21. 21.Two tanks hold 200 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  22. 22.Two tanks hold 90 litres and 105 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 400 litres and 350 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  24. 24.Three temple bells ring every 8, 4 and 30 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 10 that leaves a remainder of 2 when divided by 6, 3 or 10.
  26. 26.A hall floor is 225 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  27. 27.Kabir takes 48 seconds and Aditya 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?
  28. 28.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?
  29. 29.Sneha takes 40 seconds and Priya 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?
  30. 30.Two tanks hold 35 litres and 10 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  31. 31.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?
  32. 32.Two tanks hold 45 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  33. 33.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 5, 6 or 15.
  34. 34.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?
  35. 35.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 4, 12 or 6.
  36. 36.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?
  37. 37.Arjun takes 48 seconds and Isha 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?
  38. 38.A hall floor is 300 cm long and 240 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  39. 39.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 8, 4 or 12.
  40. 40.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?

Answer key

  1. 45
  2. 120
  3. 720
  4. 6
  5. 30
  6. 10
  7. 30
  8. 21
  9. 270
  10. 360
  11. 20
  12. 40
  13. 5
  14. 120
  15. 14
  16. 37
  17. 150
  18. 60
  19. 120
  20. 90
  21. 25
  22. 15
  23. 50
  24. 120
  25. 32
  26. 20
  27. 720
  28. 90
  29. 600
  30. 5
  31. 14
  32. 15
  33. 32
  34. 24
  35. 15
  36. 20
  37. 720
  38. 20
  39. 25
  40. 10

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