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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 188 · 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 80 litres and 180 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 25 litres and 10 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  3. 3.Tara takes 48 seconds and Arjun 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?
  4. 4.Two tanks hold 100 litres and 125 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  5. 5.Farhan takes 36 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?
  6. 6.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?
  7. 7.Three temple bells ring every 8, 30 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.Three temple bells ring every 10, 30 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 15, 9 or 5.
  10. 10.Two tanks hold 315 litres and 135 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  11. 11.Three temple bells ring every 20, 15 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.Two tanks hold 225 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  13. 13.Tara takes 30 seconds and Dev 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?
  14. 14.Two tanks hold 225 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  15. 15.Three temple bells ring every 20, 12 and 15 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 10 that leaves a remainder of 4 when divided by 6, 10 or 8.
  17. 17.Three temple bells ring every 30, 6 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 4, 3 or 12.
  19. 19.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 15, 5 or 10.
  20. 20.Three temple bells ring every 20, 5 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.Three temple bells ring every 18, 9 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Aarav takes 30 seconds and Karan takes 45 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?
  23. 23.Two tanks hold 140 litres and 160 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  24. 24.Saanvi takes 54 seconds and Ishaan 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?
  25. 25.Aarav takes 45 seconds and Meera 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?
  26. 26.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?
  27. 27.A hall floor is 175 cm long and 125 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  28. 28.Two tanks hold 75 litres and 125 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 9, 6 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.Priya takes 36 seconds and Rohan 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?
  31. 31.Diya takes 36 seconds and Nisha 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?
  32. 32.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 5, 12 or 9.
  33. 33.A hall floor is 160 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  34. 34.Two tanks hold 180 litres and 405 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  35. 35.Vivaan takes 80 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?
  36. 36.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 5, 12 or 9.
  37. 37.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?
  38. 38.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 3 or 8.
  39. 39.Three temple bells ring every 30, 20 and 5 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 12 that leaves a remainder of 1 when divided by 12, 5 or 3.

Answer key

  1. 20
  2. 5
  3. 144
  4. 25
  5. 108
  6. 14
  7. 120
  8. 60
  9. 49
  10. 45
  11. 60
  12. 25
  13. 360
  14. 25
  15. 60
  16. 124
  17. 60
  18. 14
  19. 33
  20. 60
  21. 36
  22. 90
  23. 20
  24. 432
  25. 270
  26. 24
  27. 35
  28. 25
  29. 90
  30. 360
  31. 180
  32. 181
  33. 40
  34. 45
  35. 720
  36. 182
  37. 12
  38. 121
  39. 60
  40. 61

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