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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 279 · 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 9 that leaves a remainder of 2 when divided by 3, 9 or 6.
  2. 2.Karan takes 80 seconds and Rahul 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?
  3. 3.A hall floor is 100 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  4. 4.Three temple bells ring every 20, 12 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.Two tanks hold 270 litres and 225 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 90 litres and 315 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  7. 7.Aditya takes 30 seconds and Sneha 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?
  8. 8.Three temple bells ring every 5, 18 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.Three temple bells ring every 12, 4 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.Three temple bells ring every 12, 20 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.Two tanks hold 140 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  12. 12.Sneha takes 75 seconds and Ananya 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?
  13. 13.Vivaan takes 54 seconds and Rahul 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?
  14. 14.Find the smallest number bigger than 9 that leaves a remainder of 3 when divided by 5, 4 or 9.
  15. 15.Priya takes 80 seconds and Saanvi 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?
  16. 16.Two tanks hold 315 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  17. 17.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 4, 15 or 3.
  18. 18.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 12, 15 or 5.
  19. 19.A hall floor is 315 cm long and 225 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  20. 20.Farhan takes 45 seconds and Karan 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.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 3, 12 or 8.
  22. 22.Tara takes 90 seconds and Pooja 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?
  23. 23.Sneha takes 54 seconds and Farhan 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?
  24. 24.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 5, 15 or 12.
  25. 25.Tara takes 30 seconds and Priya 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?
  26. 26.Three temple bells ring every 15, 6 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 10 or 8.
  28. 28.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 4, 10 or 6.
  29. 29.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 4, 12 or 5.
  30. 30.Find the smallest number bigger than 6 that leaves a remainder of 2 when divided by 3, 6 or 5.
  31. 31.A hall floor is 60 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  32. 32.Saanvi takes 36 seconds and Sneha 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?
  33. 33.Three temple bells ring every 18, 30 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.A hall floor is 150 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  35. 35.Two tanks hold 225 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  36. 36.Rahul takes 30 seconds and Farhan 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?
  37. 37.Two tanks hold 50 litres and 30 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 10, 24 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.Zoya takes 40 seconds and Karan 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?
  40. 40.Three temple bells ring every 30, 5 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 20
  2. 240
  3. 12
  4. 60
  5. 45
  6. 45
  7. 90
  8. 90
  9. 24
  10. 60
  11. 20
  12. 150
  13. 270
  14. 183
  15. 240
  16. 45
  17. 61
  18. 64
  19. 35
  20. 720
  21. 26
  22. 180
  23. 108
  24. 64
  25. 360
  26. 30
  27. 121
  28. 62
  29. 63
  30. 32
  31. 6
  32. 180
  33. 90
  34. 20
  35. 45
  36. 150
  37. 10
  38. 120
  39. 360
  40. 120

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