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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 282 · 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.Two tanks hold 120 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  2. 2.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?
  3. 3.A hall floor is 480 cm long and 300 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 10, 15 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.Three temple bells ring every 8, 4 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 9, 8 or 4.
  7. 7.Two tanks hold 200 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  8. 8.Three temple bells ring every 8, 6 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.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?
  10. 10.Two tanks hold 150 litres and 350 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  11. 11.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 9 or 5.
  12. 12.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?
  13. 13.Two tanks hold 80 litres and 90 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 40 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  15. 15.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?
  16. 16.Isha takes 72 seconds and Priya 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?
  17. 17.Three temple bells ring every 10, 5 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.Three temple bells ring every 15, 9 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.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?
  20. 20.Three temple bells ring every 15, 24 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.Karan takes 40 seconds and Manav 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?
  22. 22.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?
  23. 23.Karan takes 30 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?
  24. 24.Two tanks hold 30 litres and 50 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 6 that leaves a remainder of 1 when divided by 6, 3 or 4.
  26. 26.Diya takes 40 seconds and Priya 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?
  27. 27.Three temple bells ring every 8, 15 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.Three temple bells ring every 8, 12 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.A hall floor is 120 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  30. 30.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 8, 12 or 4.
  31. 31.Two tanks hold 200 litres and 320 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  32. 32.Three temple bells ring every 8, 9 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.Kavya takes 48 seconds and Aditya 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?
  34. 34.Three temple bells ring every 20, 15 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 5, 15 or 4.
  36. 36.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 8, 4 or 5.
  37. 37.Two tanks hold 250 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  38. 38.Find the smallest number bigger than 15 that leaves a remainder of 5 when divided by 15, 12 or 6.
  39. 39.A hall floor is 280 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  40. 40.A hall floor is 480 cm long and 420 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?

Answer key

  1. 30
  2. 24
  3. 40
  4. 30
  5. 72
  6. 74
  7. 25
  8. 120
  9. 120
  10. 50
  11. 46
  12. 6
  13. 10
  14. 10
  15. 28
  16. 360
  17. 120
  18. 45
  19. 12
  20. 120
  21. 120
  22. 10
  23. 180
  24. 10
  25. 13
  26. 360
  27. 120
  28. 72
  29. 12
  30. 26
  31. 40
  32. 72
  33. 240
  34. 60
  35. 62
  36. 42
  37. 50
  38. 65
  39. 35
  40. 56

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