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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 58 · 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.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 4 or 10.
  2. 2.Two tanks hold 75 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  3. 3.Two tanks hold 90 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  4. 4.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 10, 3 or 15.
  5. 5.Two tanks hold 30 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  6. 6.Two tanks hold 200 litres and 360 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  7. 7.Manav takes 40 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?
  8. 8.Two tanks hold 405 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  9. 9.Find the smallest number bigger than 6 that leaves a remainder of 2 when divided by 3, 5 or 6.
  10. 10.Three temple bells ring every 6, 18 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.Two tanks hold 20 litres and 30 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 350 litres and 300 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  13. 13.Three temple bells ring every 30, 6 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.Three temple bells ring every 18, 30 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  15. 15.Three temple bells ring every 24, 30 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.Meera takes 36 seconds and Isha 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?
  17. 17.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?
  18. 18.Sneha takes 50 seconds and Nisha 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?
  19. 19.Three temple bells ring every 4, 6 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.Two tanks hold 270 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  21. 21.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?
  22. 22.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?
  23. 23.Meera takes 54 seconds and Manav 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?
  24. 24.Farhan takes 48 seconds and Rohan 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.A hall floor is 180 cm long and 135 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  26. 26.A hall floor is 400 cm long and 350 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  27. 27.Tara takes 72 seconds and Ananya 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?
  28. 28.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 8, 4 or 15.
  29. 29.Three temple bells ring every 12, 6 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.A hall floor is 420 cm long and 300 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  31. 31.Pooja takes 80 seconds and Nisha 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?
  32. 32.Two tanks hold 60 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  33. 33.Three temple bells ring every 12, 15 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.Rohan takes 45 seconds and Pooja 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?
  35. 35.Diya takes 30 seconds and Nisha 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?
  36. 36.Vivaan takes 48 seconds and Dev 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?
  37. 37.Priya takes 36 seconds and Ananya 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?
  38. 38.Three temple bells ring every 12, 5 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.Three temple bells ring every 9, 10 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  40. 40.Manav takes 72 seconds and Sneha 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?

Answer key

  1. 62
  2. 25
  3. 30
  4. 31
  5. 10
  6. 40
  7. 360
  8. 45
  9. 32
  10. 72
  11. 10
  12. 50
  13. 90
  14. 90
  15. 120
  16. 108
  17. 28
  18. 150
  19. 36
  20. 30
  21. 21
  22. 14
  23. 432
  24. 144
  25. 12
  26. 56
  27. 360
  28. 123
  29. 24
  30. 35
  31. 720
  32. 20
  33. 60
  34. 180
  35. 240
  36. 720
  37. 108
  38. 120
  39. 90
  40. 360

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