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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 390 · 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.A hall floor is 100 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  2. 2.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?
  3. 3.Three temple bells ring every 6, 4 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.Two tanks hold 150 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  5. 5.Priya takes 45 seconds and Rohan 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?
  6. 6.Aditya takes 90 seconds and Tara 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?
  7. 7.Manav takes 40 seconds and Sneha 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?
  8. 8.A hall floor is 175 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  9. 9.Two tanks hold 35 litres and 15 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 20, 6 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.Three temple bells ring every 20, 4 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.A hall floor is 360 cm long and 225 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  13. 13.Two tanks hold 30 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 8, 6 or 12.
  15. 15.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 6, 5 or 3.
  16. 16.Arjun takes 60 seconds and Ananya 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?
  17. 17.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 10, 3 or 9.
  18. 18.Find the smallest number bigger than 5 that leaves a remainder of 1 when divided by 5, 3 or 4.
  19. 19.A hall floor is 120 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  20. 20.Three temple bells ring every 24, 9 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.Dev takes 50 seconds and Saanvi 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?
  22. 22.Two tanks hold 15 litres and 25 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  23. 23.Three temple bells ring every 30, 6 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Three temple bells ring every 5, 20 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.Three temple bells ring every 8, 24 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Saanvi takes 45 seconds and Meera 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?
  27. 27.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 8, 3 or 15.
  28. 28.A hall floor is 225 cm long and 135 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  29. 29.Two tanks hold 60 litres and 70 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  30. 30.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?
  31. 31.Isha takes 48 seconds and Pooja 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?
  32. 32.Dev takes 40 seconds and Vivaan 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?
  33. 33.A hall floor is 320 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  34. 34.Three temple bells ring every 30, 4 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.Two tanks hold 105 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  36. 36.Two tanks hold 405 litres and 360 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  37. 37.Two tanks hold 25 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  38. 38.Two tanks hold 350 litres and 250 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  39. 39.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 10, 12 or 9.
  40. 40.Three temple bells ring every 4, 8 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 12
  2. 25
  3. 60
  4. 30
  5. 225
  6. 720
  7. 120
  8. 42
  9. 5
  10. 60
  11. 40
  12. 40
  13. 15
  14. 27
  15. 31
  16. 120
  17. 91
  18. 61
  19. 6
  20. 72
  21. 150
  22. 5
  23. 90
  24. 60
  25. 72
  26. 180
  27. 121
  28. 15
  29. 10
  30. 20
  31. 144
  32. 360
  33. 24
  34. 120
  35. 15
  36. 45
  37. 5
  38. 50
  39. 182
  40. 72

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