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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 557 · 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 315 cm long and 135 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  2. 2.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?
  3. 3.Three temple bells ring every 15, 18 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.A hall floor is 125 cm long and 75 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 15 that leaves a remainder of 1 when divided by 6, 4 or 15.
  6. 6.Two tanks hold 135 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.Three temple bells ring every 10, 30 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.A hall floor is 210 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  9. 9.A hall floor is 125 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  10. 10.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?
  11. 11.Two tanks hold 135 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  12. 12.Vivaan takes 90 seconds and Aarav 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?
  13. 13.Three temple bells ring every 20, 12 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 9, 5 or 3.
  15. 15.Three temple bells ring every 12, 4 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.Three temple bells ring every 12, 20 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.Three temple bells ring every 24, 20 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.Three temple bells ring every 24, 12 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 12, 6 or 15.
  20. 20.Meera takes 30 seconds and Karan 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?
  21. 21.Sneha takes 60 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?
  22. 22.A hall floor is 175 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  23. 23.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 3 or 12.
  24. 24.Three temple bells ring every 15, 4 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.Pooja takes 75 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?
  26. 26.A hall floor is 320 cm long and 280 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  27. 27.Find the smallest number bigger than 5 that leaves a remainder of 1 when divided by 3, 5 or 4.
  28. 28.Two tanks hold 450 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  29. 29.Three temple bells ring every 15, 9 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.A hall floor is 100 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  31. 31.Two tanks hold 75 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  32. 32.A hall floor is 120 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  33. 33.Pooja takes 45 seconds and Ananya 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 210 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  35. 35.Three temple bells ring every 5, 8 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.Rahul takes 90 seconds and Pooja 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?
  37. 37.Two tanks hold 315 litres and 270 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 20, 5 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.A hall floor is 175 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  40. 40.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 3, 10 or 5.

Answer key

  1. 21
  2. 35
  3. 90
  4. 15
  5. 61
  6. 45
  7. 90
  8. 14
  9. 10
  10. 15
  11. 45
  12. 450
  13. 60
  14. 46
  15. 60
  16. 120
  17. 120
  18. 120
  19. 63
  20. 150
  21. 360
  22. 21
  23. 62
  24. 60
  25. 300
  26. 56
  27. 61
  28. 50
  29. 90
  30. 10
  31. 15
  32. 6
  33. 720
  34. 42
  35. 120
  36. 450
  37. 45
  38. 120
  39. 14
  40. 31

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