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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 540 · 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 125 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  2. 2.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 4 or 10.
  3. 3.Tara takes 90 seconds and Kabir 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?
  4. 4.Rohan takes 54 seconds and Aarav 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?
  5. 5.Three temple bells ring every 5, 9 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.Karan takes 75 seconds and Aditya 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.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 6, 8 or 9.
  8. 8.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?
  9. 9.Two tanks hold 10 litres and 25 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  10. 10.Three temple bells ring every 18, 9 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 6, 8 or 12.
  12. 12.Ishaan takes 40 seconds and Arjun 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?
  13. 13.Aditya takes 45 seconds and Tara 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?
  14. 14.Three temple bells ring every 15, 6 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  15. 15.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 5, 6 or 9.
  16. 16.Diya 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?
  17. 17.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 4, 5 or 15.
  18. 18.Three temple bells ring every 8, 6 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Three temple bells ring every 12, 30 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.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?
  21. 21.Two tanks hold 15 litres and 35 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  22. 22.Three temple bells ring every 10, 6 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.Three temple bells ring every 6, 5 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Dev takes 45 seconds and Diya 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?
  25. 25.Three temple bells ring every 8, 20 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Two tanks hold 100 litres and 250 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  27. 27.Priya takes 48 seconds and Rohan 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?
  28. 28.Two tanks hold 20 litres and 70 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  29. 29.Three temple bells ring every 24, 30 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.A hall floor is 75 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  31. 31.Two tanks hold 180 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  32. 32.Arjun takes 80 seconds and Tara 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?
  33. 33.Rohan takes 50 seconds and Farhan 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?
  34. 34.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 6, 10 or 8.
  35. 35.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?
  36. 36.Two tanks hold 125 litres and 225 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, 10 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.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?
  39. 39.A hall floor is 400 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  40. 40.Three temple bells ring every 4, 15 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 15
  2. 61
  3. 180
  4. 216
  5. 90
  6. 225
  7. 74
  8. 10
  9. 5
  10. 90
  11. 26
  12. 360
  13. 720
  14. 30
  15. 91
  16. 720
  17. 62
  18. 24
  19. 120
  20. 10
  21. 5
  22. 90
  23. 30
  24. 450
  25. 120
  26. 50
  27. 240
  28. 10
  29. 120
  30. 6
  31. 45
  32. 720
  33. 200
  34. 121
  35. 10
  36. 25
  37. 120
  38. 6
  39. 24
  40. 120

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