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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 472 · 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.Three temple bells ring every 4, 15 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 5, 4 or 12.
  3. 3.Sneha takes 54 seconds and Tara 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?
  4. 4.Three temple bells ring every 4, 10 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.Meera takes 90 seconds and Manav 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?
  6. 6.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 8, 5 or 10.
  7. 7.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 10, 9 or 15.
  8. 8.Three temple bells ring every 5, 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 8, 18 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 4, 8 or 3.
  11. 11.A hall floor is 125 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  12. 12.Arjun takes 75 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?
  13. 13.Two tanks hold 75 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.A hall floor is 100 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  15. 15.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 6, 5 or 3.
  16. 16.Three temple bells ring every 12, 5 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.Find the smallest number bigger than 5 that leaves a remainder of 1 when divided by 4, 5 or 3.
  18. 18.Three temple bells ring every 9, 18 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Three temple bells ring every 10, 15 and 5 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 9 that leaves a remainder of 2 when divided by 4, 9 or 3.
  21. 21.Two tanks hold 25 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  22. 22.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 12, 4 or 15.
  23. 23.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?
  24. 24.Three temple bells ring every 4, 15 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.A hall floor is 315 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  26. 26.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 6, 15 or 12.
  27. 27.Three temple bells ring every 5, 12 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.Two tanks hold 60 litres and 135 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 30, 10 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.Three temple bells ring every 15, 10 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.Find the smallest number bigger than 9 that leaves a remainder of 4 when divided by 9, 6 or 8.
  32. 32.Rohan takes 90 seconds and Arjun 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?
  33. 33.Karan takes 45 seconds and Dev 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.Two tanks hold 35 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  35. 35.Three temple bells ring every 30, 12 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.Two tanks hold 30 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  37. 37.Three temple bells ring every 20, 4 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.Rohan takes 60 seconds and Tara 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?
  39. 39.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?
  40. 40.Meera takes 48 seconds and Saanvi 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?

Answer key

  1. 60
  2. 63
  3. 270
  4. 40
  5. 360
  6. 43
  7. 91
  8. 90
  9. 72
  10. 25
  11. 15
  12. 600
  13. 25
  14. 15
  15. 31
  16. 120
  17. 61
  18. 36
  19. 30
  20. 38
  21. 5
  22. 61
  23. 30
  24. 120
  25. 14
  26. 61
  27. 60
  28. 15
  29. 60
  30. 60
  31. 76
  32. 720
  33. 270
  34. 5
  35. 60
  36. 10
  37. 60
  38. 240
  39. 30
  40. 720

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