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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 5 · 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 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 210 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  3. 3.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 3, 4 or 8.
  4. 4.Saanvi takes 75 seconds and Priya 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?
  5. 5.Find the smallest number bigger than 6 that leaves a remainder of 3 when divided by 4, 5 or 6.
  6. 6.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 4, 12 or 3.
  7. 7.Two tanks hold 300 litres and 250 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  8. 8.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?
  9. 9.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 5, 15 or 3.
  10. 10.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?
  11. 11.Three temple bells ring every 5, 6 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.Two tanks hold 140 litres and 60 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 24, 6 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.A hall floor is 250 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  15. 15.Three temple bells ring every 30, 20 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.Three temple bells ring every 15, 24 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.Zoya takes 80 seconds and Aarav 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?
  18. 18.Karan takes 60 seconds and Tara 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?
  19. 19.A hall floor is 200 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  20. 20.Tara takes 54 seconds and Sneha 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?
  21. 21.Three temple bells ring every 5, 6 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.A hall floor is 140 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  23. 23.Three temple bells ring every 15, 30 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Karan takes 60 seconds and Rohan 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?
  25. 25.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 4 or 3.
  26. 26.Zoya takes 40 seconds and Dev 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?
  27. 27.Karan takes 75 seconds and Vivaan 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?
  28. 28.Three temple bells ring every 12, 4 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Tara takes 50 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?
  30. 30.Two tanks hold 405 litres and 315 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 480 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  32. 32.Two tanks hold 135 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  33. 33.Zoya takes 45 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?
  34. 34.Three temple bells ring every 5, 8 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.Two tanks hold 315 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  36. 36.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 10 or 8.
  37. 37.Find the smallest number bigger than 6 that leaves a remainder of 2 when divided by 4, 6 or 5.
  38. 38.Three temple bells ring every 8, 18 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.Vivaan takes 75 seconds and Pooja 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?
  40. 40.Three temple bells ring every 6, 24 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 20
  2. 30
  3. 26
  4. 300
  5. 63
  6. 13
  7. 50
  8. 5
  9. 16
  10. 40
  11. 60
  12. 20
  13. 120
  14. 10
  15. 120
  16. 120
  17. 720
  18. 300
  19. 24
  20. 270
  21. 90
  22. 28
  23. 60
  24. 240
  25. 14
  26. 120
  27. 300
  28. 60
  29. 150
  30. 45
  31. 24
  32. 45
  33. 180
  34. 120
  35. 45
  36. 121
  37. 62
  38. 72
  39. 450
  40. 72

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