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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 32 · 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 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?
  2. 2.Two tanks hold 90 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  3. 3.Kavya takes 90 seconds and Meera 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?
  4. 4.Two tanks hold 10 litres and 35 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 8 that leaves a remainder of 1 when divided by 8, 6 or 3.
  6. 6.Two tanks hold 100 litres and 350 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  7. 7.Two tanks hold 80 litres and 280 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  8. 8.Dev takes 40 seconds and Farhan 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?
  9. 9.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?
  10. 10.Two tanks hold 75 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  11. 11.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?
  12. 12.Three temple bells ring every 18, 5 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.A hall floor is 280 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  14. 14.Kabir takes 30 seconds and Zoya 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 30, 4 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.Two tanks hold 60 litres and 135 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  17. 17.Three temple bells ring every 18, 30 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.Three temple bells ring every 9, 8 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Three temple bells ring every 15, 4 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.Meera takes 60 seconds and Dev 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?
  21. 21.A hall floor is 200 cm long and 175 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  22. 22.Kabir takes 45 seconds and Sneha 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?
  23. 23.A hall floor is 100 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  24. 24.Three temple bells ring every 5, 12 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.Three temple bells ring every 12, 6 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.A hall floor is 160 cm long and 140 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  27. 27.A hall floor is 210 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  28. 28.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 3 or 8.
  29. 29.Tara takes 45 seconds and Karan 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?
  30. 30.Two tanks hold 350 litres and 450 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  31. 31.Three temple bells ring every 12, 8 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 3, 10 or 15.
  33. 33.Three temple bells ring every 9, 30 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.Three temple bells ring every 10, 12 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.Three temple bells ring every 5, 6 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.Two tanks hold 80 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  37. 37.Three temple bells ring every 6, 8 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.Kabir takes 54 seconds and Ananya 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?
  39. 39.Three temple bells ring every 15, 18 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  40. 40.Three temple bells ring every 4, 5 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 10
  2. 10
  3. 180
  4. 5
  5. 25
  6. 50
  7. 40
  8. 120
  9. 28
  10. 15
  11. 24
  12. 90
  13. 21
  14. 120
  15. 60
  16. 15
  17. 90
  18. 72
  19. 120
  20. 240
  21. 56
  22. 180
  23. 10
  24. 120
  25. 60
  26. 56
  27. 28
  28. 26
  29. 180
  30. 50
  31. 24
  32. 31
  33. 90
  34. 60
  35. 90
  36. 10
  37. 120
  38. 432
  39. 90
  40. 40

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