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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 164 · 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 50 litres and 40 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 35 litres and 30 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 140 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  4. 4.Pooja takes 90 seconds and Rohan 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?
  5. 5.Two tanks hold 100 litres and 80 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 20, 5 and 30 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 15 that leaves a remainder of 3 when divided by 6, 8 or 15.
  8. 8.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 3, 15 or 4.
  9. 9.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 12, 15 or 6.
  10. 10.Meera takes 40 seconds and Nisha 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?
  11. 11.Three temple bells ring every 20, 24 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.Three temple bells ring every 10, 8 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.Priya takes 45 seconds and Dev 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?
  14. 14.Aditya takes 72 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?
  15. 15.Three temple bells ring every 8, 12 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.Three temple bells ring every 4, 5 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 8, 10 or 15.
  18. 18.A hall floor is 280 cm long and 160 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  19. 19.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 3, 12 or 15.
  20. 20.Aditya takes 48 seconds and Diya 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?
  21. 21.A hall floor is 420 cm long and 360 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  22. 22.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 4, 9 or 8.
  23. 23.Three temple bells ring every 18, 8 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Two tanks hold 100 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  25. 25.Two tanks hold 100 litres and 250 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  26. 26.Three temple bells ring every 9, 15 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.A hall floor is 150 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  28. 28.Sneha takes 72 seconds and Diya 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?
  29. 29.A hall floor is 120 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  30. 30.Two tanks hold 45 litres and 35 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  31. 31.Nisha takes 36 seconds and Aditya 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?
  32. 32.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 3, 10 or 12.
  33. 33.Two tanks hold 100 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  34. 34.A hall floor is 360 cm long and 315 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  35. 35.A hall floor is 315 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  36. 36.Three temple bells ring every 8, 18 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  37. 37.Arjun takes 45 seconds and Nisha 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?
  38. 38.Three temple bells ring every 6, 4 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.Saanvi takes 48 seconds and Meera 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?
  40. 40.Find the smallest number bigger than 8 that leaves a remainder of 4 when divided by 5, 6 or 8.

Answer key

  1. 10
  2. 5
  3. 14
  4. 360
  5. 20
  6. 60
  7. 123
  8. 61
  9. 63
  10. 360
  11. 120
  12. 120
  13. 270
  14. 360
  15. 72
  16. 20
  17. 121
  18. 28
  19. 61
  20. 432
  21. 42
  22. 74
  23. 72
  24. 25
  25. 50
  26. 45
  27. 10
  28. 216
  29. 12
  30. 5
  31. 720
  32. 61
  33. 20
  34. 56
  35. 14
  36. 72
  37. 90
  38. 60
  39. 240
  40. 124

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