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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 391 · 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).

NameDateTime takenScore ___ / 40
  1. 1.A hall floor is 175 cm long and 125 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  2. 2.Two tanks hold 80 litres and 140 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  3. 3.Three temple bells ring every 12, 9 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.Sneha takes 48 seconds and Manav 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?
  5. 5.Two tanks hold 100 litres and 450 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  6. 6.Tara takes 36 seconds and Aarav 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?
  7. 7.Arjun takes 36 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?
  8. 8.Two tanks hold 75 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  9. 9.Three temple bells ring every 15, 18 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.Arjun takes 50 seconds and Rohan 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?
  11. 11.A hall floor is 210 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  12. 12.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 3, 9 or 12.
  13. 13.Three temple bells ring every 5, 30 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.A hall floor is 180 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  15. 15.Two tanks hold 240 litres and 270 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  16. 16.Manav takes 36 seconds and Diya 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?
  17. 17.Two tanks hold 175 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  18. 18.Kavya takes 30 seconds and Isha 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?
  19. 19.Sneha takes 60 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?
  20. 20.Three temple bells ring every 24, 15 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.Three temple bells ring every 5, 4 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Arjun takes 30 seconds and Saanvi 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?
  23. 23.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?
  24. 24.A hall floor is 350 cm long and 250 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  25. 25.A hall floor is 360 cm long and 300 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  26. 26.Three temple bells ring every 5, 30 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.Three temple bells ring every 15, 12 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.Ishaan takes 45 seconds and Karan 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?
  29. 29.Three temple bells ring every 30, 8 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.Two tanks hold 20 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  31. 31.Ishaan takes 45 seconds and Isha 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?
  32. 32.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 9, 8 or 12.
  33. 33.Meera takes 60 seconds and Pooja 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?
  34. 34.A hall floor is 125 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  35. 35.Nisha takes 50 seconds and Karan 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?
  36. 36.A hall floor is 225 cm long and 135 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  37. 37.A hall floor is 210 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  38. 38.Nisha takes 45 seconds and Rahul 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?
  39. 39.Farhan takes 45 seconds and Vivaan 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?
  40. 40.Dev takes 30 seconds and Meera 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. 35
  2. 20
  3. 72
  4. 720
  5. 50
  6. 360
  7. 180
  8. 15
  9. 90
  10. 300
  11. 21
  12. 37
  13. 120
  14. 30
  15. 30
  16. 180
  17. 25
  18. 240
  19. 240
  20. 120
  21. 60
  22. 360
  23. 28
  24. 35
  25. 30
  26. 120
  27. 60
  28. 360
  29. 120
  30. 10
  31. 180
  32. 73
  33. 240
  34. 20
  35. 150
  36. 15
  37. 35
  38. 450
  39. 720
  40. 360

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