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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 160 · 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 150 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 30, 20 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.Aarav takes 48 seconds and Pooja 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.A hall floor is 320 cm long and 280 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 10, 20 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 3, 5 or 6.
  7. 7.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?
  8. 8.Aditya takes 36 seconds and Sneha 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?
  9. 9.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 4, 12 or 3.
  10. 10.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?
  11. 11.A hall floor is 240 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  12. 12.Two tanks hold 225 litres and 175 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  13. 13.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?
  14. 14.Two tanks hold 60 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  15. 15.Three temple bells ring every 10, 30 and 20 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, 10 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.Two tanks hold 45 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  18. 18.Three temple bells ring every 8, 30 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Two tanks hold 200 litres and 160 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  20. 20.Three temple bells ring every 5, 24 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.Dev takes 75 seconds and Meera 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?
  22. 22.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 5, 15 or 12.
  23. 23.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 4, 5 or 10.
  24. 24.Three temple bells ring every 12, 5 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 9 that leaves a remainder of 1 when divided by 9, 8 or 3.
  26. 26.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 4, 6 or 3.
  27. 27.Three temple bells ring every 8, 4 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.Three temple bells ring every 12, 8 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Diya takes 48 seconds and Pooja 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?
  30. 30.Three temple bells ring every 30, 15 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.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?
  32. 32.Two tanks hold 80 litres and 140 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  33. 33.Three temple bells ring every 15, 6 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.Two tanks hold 360 litres and 315 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  35. 35.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 5, 6 or 8.
  36. 36.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?
  37. 37.Tara takes 36 seconds and Saanvi 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?
  38. 38.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 9, 10 or 15.
  39. 39.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 10, 12 or 15.
  40. 40.Two tanks hold 150 litres and 175 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?

Answer key

  1. 50
  2. 60
  3. 240
  4. 56
  5. 60
  6. 31
  7. 6
  8. 108
  9. 13
  10. 10
  11. 24
  12. 25
  13. 40
  14. 20
  15. 60
  16. 60
  17. 5
  18. 120
  19. 40
  20. 120
  21. 225
  22. 61
  23. 22
  24. 60
  25. 73
  26. 13
  27. 72
  28. 72
  29. 240
  30. 60
  31. 45
  32. 20
  33. 120
  34. 45
  35. 122
  36. 14
  37. 720
  38. 92
  39. 64
  40. 25

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