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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 314 · 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 250 litres and 350 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  2. 2.Two tanks hold 140 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  3. 3.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?
  4. 4.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 12 or 8.
  5. 5.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 9, 3 or 5.
  6. 6.Two tanks hold 60 litres and 210 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  7. 7.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 15, 8 or 10.
  8. 8.Three temple bells ring every 20, 24 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.Two tanks hold 250 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  10. 10.Three temple bells ring every 8, 24 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 8, 12 or 15.
  12. 12.Dev takes 45 seconds and Ananya 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?
  13. 13.Two tanks hold 90 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.Diya takes 48 seconds and Kabir 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?
  15. 15.Three temple bells ring every 24, 15 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.Find the smallest number bigger than 9 that leaves a remainder of 3 when divided by 9, 6 or 5.
  17. 17.A hall floor is 140 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  18. 18.A hall floor is 140 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  19. 19.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?
  20. 20.Pooja takes 40 seconds and Isha 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?
  21. 21.Three temple bells ring every 24, 4 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Three temple bells ring every 15, 30 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.Farhan takes 50 seconds and Sneha 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?
  24. 24.Priya takes 90 seconds and Vivaan 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?
  25. 25.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?
  26. 26.A hall floor is 210 cm long and 90 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 15 that leaves a remainder of 2 when divided by 15, 5 or 4.
  28. 28.Find the smallest number bigger than 5 that leaves a remainder of 1 when divided by 3, 5 or 4.
  29. 29.Three temple bells ring every 15, 4 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.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?
  31. 31.Isha takes 72 seconds and Rohan 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?
  32. 32.Three temple bells ring every 8, 4 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.Sneha takes 90 seconds and Zoya 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?
  34. 34.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 3, 8 or 9.
  35. 35.A hall floor is 80 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  36. 36.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 4, 10 or 9.
  37. 37.Two tanks hold 20 litres and 70 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  38. 38.Two tanks hold 120 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  39. 39.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 3, 10 or 4.
  40. 40.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 6 or 4.

Answer key

  1. 50
  2. 20
  3. 15
  4. 121
  5. 46
  6. 30
  7. 124
  8. 120
  9. 50
  10. 120
  11. 123
  12. 180
  13. 15
  14. 144
  15. 120
  16. 93
  17. 35
  18. 14
  19. 42
  20. 360
  21. 72
  22. 60
  23. 450
  24. 180
  25. 40
  26. 21
  27. 62
  28. 61
  29. 120
  30. 14
  31. 720
  32. 24
  33. 270
  34. 73
  35. 12
  36. 181
  37. 10
  38. 15
  39. 61
  40. 13

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