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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 154 · 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.Three temple bells ring every 20, 5 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.Three temple bells ring every 5, 24 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.Sneha takes 90 seconds and Tara 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?
  4. 4.Two tanks hold 90 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  5. 5.Ishaan takes 75 seconds and Nisha 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?
  6. 6.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 5, 3 or 15.
  7. 7.Find the smallest number bigger than 9 that leaves a remainder of 5 when divided by 9, 6 or 8.
  8. 8.Find the smallest number bigger than 12 that leaves a remainder of 4 when divided by 6, 9 or 12.
  9. 9.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?
  10. 10.Three temple bells ring every 5, 18 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.Three temple bells ring every 30, 20 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 10, 4 or 3.
  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.Three temple bells ring every 12, 10 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  15. 15.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?
  16. 16.Two tanks hold 135 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  17. 17.Two tanks hold 40 litres and 140 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  18. 18.Two tanks hold 80 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  19. 19.A hall floor is 240 cm long and 200 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 10, 6 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.Three temple bells ring every 4, 6 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Find the smallest number bigger than 12 that leaves a remainder of 5 when divided by 10, 8 or 12.
  23. 23.Aarav takes 75 seconds and Priya 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?
  24. 24.Two tanks hold 250 litres and 300 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  25. 25.Three temple bells ring every 20, 10 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.A hall floor is 240 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  27. 27.Two tanks hold 30 litres and 70 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  28. 28.Three temple bells ring every 8, 30 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.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?
  30. 30.Two tanks hold 135 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  31. 31.Farhan takes 60 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?
  32. 32.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 3, 12 or 15.
  33. 33.Sneha takes 50 seconds and Kavya 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?
  34. 34.Diya takes 72 seconds and Kavya 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.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?
  36. 36.Three temple bells ring every 8, 5 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  37. 37.Priya takes 54 seconds and Dev 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?
  38. 38.Three temple bells ring every 24, 5 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.Three temple bells ring every 24, 18 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  40. 40.Kabir takes 50 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?

Answer key

  1. 60
  2. 120
  3. 180
  4. 10
  5. 225
  6. 16
  7. 77
  8. 40
  9. 35
  10. 90
  11. 60
  12. 62
  13. 10
  14. 60
  15. 21
  16. 45
  17. 20
  18. 20
  19. 30
  20. 90
  21. 60
  22. 125
  23. 150
  24. 50
  25. 60
  26. 24
  27. 10
  28. 120
  29. 15
  30. 15
  31. 120
  32. 61
  33. 150
  34. 216
  35. 15
  36. 120
  37. 270
  38. 120
  39. 72
  40. 300

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