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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 539 · 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 200 cm long and 150 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 2 when divided by 8, 15 or 12.
  3. 3.A hall floor is 300 cm long and 250 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 6, 5 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.Nisha takes 36 seconds and Ananya 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?
  6. 6.Three temple bells ring every 5, 4 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.A hall floor is 250 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  8. 8.A hall floor is 150 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  9. 9.Diya takes 45 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?
  10. 10.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?
  11. 11.A hall floor is 480 cm long and 180 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 1 when divided by 5, 15 or 3.
  13. 13.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 6, 12 or 5.
  14. 14.Two tanks hold 320 litres and 200 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 280 litres and 160 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 225 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  17. 17.Aarav takes 36 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?
  18. 18.Three temple bells ring every 9, 12 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Two tanks hold 90 litres and 210 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  20. 20.Zoya takes 36 seconds and Pooja 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.A hall floor is 100 cm long and 80 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 15, 6 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.Three temple bells ring every 24, 5 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Two tanks hold 15 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  25. 25.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 5, 4 or 15.
  26. 26.Three temple bells ring every 24, 15 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.Rohan takes 40 seconds and Sneha 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?
  28. 28.Three temple bells ring every 30, 12 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Find the smallest number bigger than 15 that leaves a remainder of 5 when divided by 15, 6 or 8.
  30. 30.Rohan takes 40 seconds and Rahul 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?
  31. 31.A hall floor is 300 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  32. 32.A hall floor is 350 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  33. 33.Two tanks hold 320 litres and 280 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  34. 34.A hall floor is 250 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  35. 35.Two tanks hold 90 litres and 225 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 40 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  37. 37.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 5, 8 or 4.
  38. 38.Arjun takes 48 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?
  39. 39.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?
  40. 40.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 8, 5 or 4.

Answer key

  1. 12
  2. 122
  3. 30
  4. 120
  5. 180
  6. 60
  7. 15
  8. 10
  9. 270
  10. 10
  11. 24
  12. 16
  13. 63
  14. 40
  15. 40
  16. 10
  17. 180
  18. 36
  19. 30
  20. 144
  21. 20
  22. 60
  23. 120
  24. 5
  25. 61
  26. 120
  27. 240
  28. 60
  29. 125
  30. 120
  31. 15
  32. 28
  33. 40
  34. 20
  35. 45
  36. 5
  37. 41
  38. 240
  39. 120
  40. 41

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