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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 241 · 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 320 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  2. 2.A hall floor is 315 cm long and 135 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  3. 3.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 5, 12 or 15.
  4. 4.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?
  5. 5.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 3 or 6.
  6. 6.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 10 or 4.
  7. 7.Rahul takes 80 seconds and Aditya 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?
  8. 8.Two tanks hold 60 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  9. 9.Rohan takes 36 seconds and Farhan 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?
  10. 10.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 3 or 9.
  11. 11.A hall floor is 200 cm long and 150 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 15 that leaves a remainder of 2 when divided by 4, 6 or 15.
  13. 13.Two tanks hold 75 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.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?
  15. 15.Two tanks hold 30 litres and 105 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  16. 16.A hall floor is 315 cm long and 270 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  17. 17.Two tanks hold 60 litres and 135 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  18. 18.Arjun takes 40 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?
  19. 19.Two tanks hold 150 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  20. 20.Three temple bells ring every 15, 18 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.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?
  22. 22.Three temple bells ring every 30, 4 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.Two tanks hold 360 litres and 405 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 3 when divided by 15, 4 or 6.
  25. 25.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?
  26. 26.Two tanks hold 80 litres and 180 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 60 seconds and Zoya 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?
  28. 28.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 6, 4 or 9.
  29. 29.Two tanks hold 315 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  30. 30.Diya takes 40 seconds and Aarav 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?
  31. 31.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 8, 15 or 3.
  32. 32.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 8, 12 or 9.
  33. 33.Vivaan takes 90 seconds and Sneha 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.Three temple bells ring every 10, 5 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.Vivaan takes 30 seconds and Isha 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?
  36. 36.A hall floor is 240 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  37. 37.A hall floor is 150 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  38. 38.Three temple bells ring every 5, 6 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.Three temple bells ring every 8, 20 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  40. 40.A hall floor is 200 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?

Answer key

  1. 24
  2. 21
  3. 64
  4. 12
  5. 14
  6. 61
  7. 240
  8. 30
  9. 180
  10. 38
  11. 12
  12. 62
  13. 25
  14. 30
  15. 15
  16. 42
  17. 15
  18. 120
  19. 30
  20. 90
  21. 28
  22. 60
  23. 45
  24. 63
  25. 35
  26. 20
  27. 180
  28. 37
  29. 45
  30. 360
  31. 122
  32. 75
  33. 720
  34. 90
  35. 150
  36. 30
  37. 15
  38. 60
  39. 120
  40. 24

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