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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 30 · 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 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  2. 2.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 8, 3 or 6.
  3. 3.Arjun takes 60 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?
  4. 4.Two tanks hold 40 litres and 25 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  5. 5.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 10, 6 or 5.
  6. 6.Three temple bells ring every 6, 5 and 18 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 9 that leaves a remainder of 4 when divided by 5, 6 or 9.
  8. 8.A hall floor is 225 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  9. 9.Nisha takes 90 seconds and Tara 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?
  10. 10.Two tanks hold 135 litres and 360 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  11. 11.Farhan takes 60 seconds and Zoya 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?
  12. 12.Three temple bells ring every 9, 10 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.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?
  14. 14.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?
  15. 15.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 9, 4 or 3.
  16. 16.A hall floor is 360 cm long and 135 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 9, 8 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 4, 9 or 10.
  19. 19.Two tanks hold 160 litres and 100 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 4, 6 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 10, 6 or 9.
  22. 22.Two tanks hold 320 litres and 280 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  23. 23.Nisha takes 90 seconds and Farhan 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?
  24. 24.Vivaan takes 54 seconds and Dev 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?
  25. 25.Three temple bells ring every 5, 8 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Three temple bells ring every 6, 9 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.A hall floor is 300 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  28. 28.Three temple bells ring every 10, 12 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Two tanks hold 80 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  30. 30.Three temple bells ring every 4, 30 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.Two tanks hold 60 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  32. 32.Three temple bells ring every 6, 9 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.A hall floor is 90 cm long and 60 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 9, 6 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.Two tanks hold 225 litres and 270 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  36. 36.Three temple bells ring every 10, 20 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  37. 37.A hall floor is 200 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  38. 38.Ananya takes 40 seconds and Ishaan 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?
  39. 39.A hall floor is 350 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  40. 40.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 9, 5 or 3.

Answer key

  1. 25
  2. 26
  3. 240
  4. 5
  5. 32
  6. 90
  7. 94
  8. 10
  9. 270
  10. 45
  11. 300
  12. 90
  13. 14
  14. 10
  15. 38
  16. 24
  17. 72
  18. 181
  19. 20
  20. 24
  21. 93
  22. 40
  23. 360
  24. 108
  25. 40
  26. 72
  27. 15
  28. 120
  29. 20
  30. 60
  31. 10
  32. 36
  33. 6
  34. 90
  35. 45
  36. 120
  37. 15
  38. 360
  39. 21
  40. 47

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