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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 212 · 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 50 litres and 40 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 180 cm long and 120 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 10, 12 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.Two tanks hold 270 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  5. 5.Saanvi takes 72 seconds and Rohan 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.Rohan takes 72 seconds and Diya 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?
  7. 7.Two tanks hold 120 litres and 210 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 4, 6 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.Three temple bells ring every 9, 5 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.Three temple bells ring every 5, 15 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.Two tanks hold 200 litres and 240 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  12. 12.A hall floor is 300 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  13. 13.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 5, 9 or 3.
  14. 14.Three temple bells ring every 8, 9 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  15. 15.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 10, 15 or 5.
  16. 16.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 3, 10 or 12.
  17. 17.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 15, 6 or 9.
  18. 18.Two tanks hold 225 litres and 125 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  19. 19.Three temple bells ring every 15, 5 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.Vivaan takes 60 seconds and Aditya 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.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 3, 5 or 12.
  22. 22.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?
  23. 23.Find the smallest number bigger than 6 that leaves a remainder of 3 when divided by 5, 4 or 6.
  24. 24.A hall floor is 280 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  25. 25.Three temple bells ring every 10, 15 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.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?
  27. 27.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?
  28. 28.Three temple bells ring every 6, 8 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Three temple bells ring every 30, 10 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.A hall floor is 160 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  31. 31.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?
  32. 32.Two tanks hold 35 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  33. 33.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 5, 6 or 15.
  34. 34.Aditya takes 45 seconds and Tara 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?
  35. 35.Three temple bells ring every 24, 15 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 8, 10 or 12.
  37. 37.Two tanks hold 50 litres and 175 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  38. 38.Pooja takes 40 seconds and Karan 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?
  39. 39.Aarav takes 45 seconds and Vivaan 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?
  40. 40.Tara takes 60 seconds and Zoya 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?

Answer key

  1. 10
  2. 6
  3. 60
  4. 30
  5. 360
  6. 144
  7. 30
  8. 36
  9. 45
  10. 90
  11. 40
  12. 10
  13. 46
  14. 72
  15. 33
  16. 61
  17. 93
  18. 25
  19. 90
  20. 180
  21. 62
  22. 35
  23. 63
  24. 21
  25. 120
  26. 15
  27. 56
  28. 120
  29. 120
  30. 24
  31. 12
  32. 5
  33. 32
  34. 270
  35. 120
  36. 121
  37. 25
  38. 120
  39. 720
  40. 360

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