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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 379 · 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 180 litres and 150 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 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?
  3. 3.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?
  4. 4.Meera takes 80 seconds and Saanvi 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?
  5. 5.Two tanks hold 120 litres and 160 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  6. 6.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?
  7. 7.Two tanks hold 360 litres and 405 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  8. 8.A hall floor is 300 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  9. 9.A hall floor is 350 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  10. 10.Nisha takes 48 seconds and Pooja 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?
  11. 11.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 3, 6 or 8.
  12. 12.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 10 or 5.
  13. 13.Ananya takes 36 seconds and Pooja 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.Vivaan takes 90 seconds and Diya 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?
  15. 15.Three temple bells ring every 12, 5 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.A hall floor is 420 cm long and 300 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  17. 17.Three temple bells ring every 24, 5 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.A hall floor is 400 cm long and 350 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  19. 19.Ishaan takes 90 seconds and Vivaan 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?
  20. 20.Three temple bells ring every 4, 6 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.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?
  22. 22.Two tanks hold 250 litres and 450 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 225 litres and 405 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  24. 24.A hall floor is 125 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  25. 25.Two tanks hold 35 litres and 25 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  26. 26.Two tanks hold 125 litres and 175 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  27. 27.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?
  28. 28.Diya takes 30 seconds and Meera 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?
  29. 29.A hall floor is 60 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  30. 30.Two tanks hold 10 litres and 25 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  31. 31.Isha takes 90 seconds and Ananya 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 315 cm long and 225 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  33. 33.Three temple bells ring every 5, 24 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.Three temple bells ring every 20, 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 15 that leaves a remainder of 4 when divided by 6, 15 or 9.
  36. 36.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?
  37. 37.Diya takes 40 seconds and Saanvi 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?
  38. 38.Aditya takes 75 seconds and Vivaan 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?
  39. 39.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 3, 4 or 15.
  40. 40.Two tanks hold 60 litres and 140 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?

Answer key

  1. 30
  2. 15
  3. 10
  4. 720
  5. 40
  6. 15
  7. 45
  8. 10
  9. 14
  10. 240
  11. 25
  12. 31
  13. 180
  14. 180
  15. 60
  16. 35
  17. 120
  18. 56
  19. 360
  20. 36
  21. 20
  22. 50
  23. 45
  24. 20
  25. 5
  26. 25
  27. 10
  28. 120
  29. 6
  30. 5
  31. 450
  32. 35
  33. 120
  34. 60
  35. 94
  36. 21
  37. 120
  38. 150
  39. 61
  40. 20

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