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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 265 · 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.A hall floor is 240 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  2. 2.Three temple bells ring every 15, 5 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.Two tanks hold 90 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  4. 4.Three temple bells ring every 4, 15 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.Three temple bells ring every 5, 4 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.Isha takes 50 seconds and Ishaan 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?
  7. 7.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?
  8. 8.Two tanks hold 100 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  9. 9.Two tanks hold 30 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  10. 10.Aarav takes 90 seconds and Zoya 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?
  11. 11.Two tanks hold 90 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  12. 12.Two tanks hold 210 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.Two tanks hold 135 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.Rahul takes 90 seconds and Saanvi 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.A hall floor is 300 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  16. 16.Three temple bells ring every 6, 15 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.A hall floor is 160 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  18. 18.Two tanks hold 70 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  19. 19.Karan takes 90 seconds and Arjun 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?
  20. 20.Find the smallest number bigger than 5 that leaves a remainder of 2 when divided by 3, 4 or 5.
  21. 21.Three temple bells ring every 18, 4 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Priya takes 90 seconds and Ananya 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.Two tanks hold 70 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  24. 24.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 9, 15 or 6.
  25. 25.Three temple bells ring every 15, 4 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 12, 15 or 6.
  27. 27.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?
  28. 28.Three temple bells ring every 5, 20 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Nisha takes 90 seconds and Aarav 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?
  30. 30.Ananya takes 60 seconds and Karan 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?
  31. 31.Three temple bells ring every 4, 10 and 24 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 2 when divided by 9, 3 or 15.
  33. 33.Two tanks hold 315 litres and 135 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 175 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  35. 35.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 3, 6 or 12.
  36. 36.A hall floor is 140 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  37. 37.Two tanks hold 180 litres and 315 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  38. 38.Three temple bells ring every 15, 6 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.Two tanks hold 225 litres and 315 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  40. 40.Tara takes 45 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?

Answer key

  1. 40
  2. 45
  3. 30
  4. 60
  5. 60
  6. 450
  7. 28
  8. 25
  9. 15
  10. 720
  11. 10
  12. 30
  13. 15
  14. 360
  15. 10
  16. 60
  17. 40
  18. 10
  19. 450
  20. 62
  21. 72
  22. 180
  23. 10
  24. 94
  25. 60
  26. 63
  27. 56
  28. 60
  29. 720
  30. 300
  31. 120
  32. 47
  33. 45
  34. 42
  35. 13
  36. 35
  37. 45
  38. 60
  39. 45
  40. 360

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