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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 185 · 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).

NameDateTime takenScore ___ / 40
  1. 1.Find the smallest number bigger than 6 that leaves a remainder of 2 when divided by 3, 4 or 6.
  2. 2.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?
  3. 3.Three temple bells ring every 6, 10 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.Three temple bells ring every 15, 24 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.Three temple bells ring every 12, 6 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.Three temple bells ring every 6, 20 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.Three temple bells ring every 12, 15 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.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?
  9. 9.Two tanks hold 360 litres and 405 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 6, 9 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.Three temple bells ring every 4, 15 and 5 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 12 that leaves a remainder of 3 when divided by 5, 4 or 12.
  13. 13.Ananya takes 75 seconds and Pooja 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?
  14. 14.Karan takes 60 seconds and Rohan 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.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?
  16. 16.Two tanks hold 90 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  17. 17.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 8, 12 or 3.
  18. 18.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 4, 9 or 5.
  19. 19.Three temple bells ring every 10, 6 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.Find the smallest number bigger than 5 that leaves a remainder of 2 when divided by 3, 4 or 5.
  21. 21.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?
  22. 22.Three temple bells ring every 12, 6 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.Ishaan takes 36 seconds and Rahul 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?
  24. 24.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?
  25. 25.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 6, 9 or 3.
  26. 26.Three temple bells ring every 8, 12 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.Rohan takes 36 seconds and Aarav 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?
  28. 28.Find the smallest number bigger than 9 that leaves a remainder of 3 when divided by 8, 6 or 9.
  29. 29.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 10, 15 or 3.
  30. 30.Arjun takes 90 seconds and Ananya takes 50 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 80 seconds and Rahul 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?
  32. 32.Three temple bells ring every 5, 20 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.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?
  34. 34.Three temple bells ring every 6, 8 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.Two tanks hold 135 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  36. 36.Aarav takes 30 seconds and Priya 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?
  37. 37.Two tanks hold 240 litres and 90 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 12 that leaves a remainder of 3 when divided by 8, 9 or 12.
  39. 39.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 3 or 6.
  40. 40.Two tanks hold 60 litres and 105 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?

Answer key

  1. 14
  2. 120
  3. 90
  4. 120
  5. 36
  6. 60
  7. 60
  8. 24
  9. 45
  10. 90
  11. 60
  12. 63
  13. 225
  14. 180
  15. 5
  16. 45
  17. 26
  18. 181
  19. 90
  20. 62
  21. 10
  22. 60
  23. 108
  24. 15
  25. 20
  26. 24
  27. 180
  28. 75
  29. 32
  30. 450
  31. 720
  32. 60
  33. 10
  34. 120
  35. 45
  36. 90
  37. 30
  38. 75
  39. 13
  40. 15

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