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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 263 · 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 15 that leaves a remainder of 2 when divided by 5, 10 or 15.
  2. 2.Three temple bells ring every 12, 20 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 4, 15 or 10.
  4. 4.Two tanks hold 25 litres and 35 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  5. 5.Three temple bells ring every 6, 24 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.Two tanks hold 80 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  7. 7.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 4, 9 or 5.
  8. 8.Tara takes 45 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?
  9. 9.Dev takes 30 seconds and Ananya 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?
  10. 10.Find the smallest number bigger than 8 that leaves a remainder of 3 when divided by 4, 8 or 6.
  11. 11.Diya takes 48 seconds and Rahul 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?
  12. 12.Three temple bells ring every 20, 15 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 5, 15 or 10.
  14. 14.Two tanks hold 90 litres and 60 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, 30 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.Two tanks hold 40 litres and 100 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 10, 12 or 3.
  18. 18.Two tanks hold 405 litres and 90 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 8, 12 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.Rohan takes 48 seconds and Rahul 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?
  21. 21.Three temple bells ring every 8, 30 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Two tanks hold 45 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  23. 23.Three temple bells ring every 18, 10 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Three temple bells ring every 15, 9 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.Manav takes 30 seconds and Ishaan 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.Three temple bells ring every 10, 4 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.Dev takes 30 seconds and Meera 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?
  28. 28.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 3, 12 or 5.
  29. 29.Three temple bells ring every 15, 6 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.Diya takes 40 seconds and Zoya 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?
  31. 31.Two tanks hold 405 litres and 315 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  32. 32.Diya takes 60 seconds and Karan 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?
  33. 33.A hall floor is 100 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  34. 34.Three temple bells ring every 18, 9 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.Two tanks hold 150 litres and 90 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 15, 9 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  37. 37.A hall floor is 140 cm long and 100 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 12 that leaves a remainder of 1 when divided by 12, 4 or 5.
  39. 39.Two tanks hold 60 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  40. 40.Two tanks hold 140 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?

Answer key

  1. 32
  2. 60
  3. 62
  4. 5
  5. 72
  6. 10
  7. 182
  8. 90
  9. 90
  10. 27
  11. 720
  12. 120
  13. 32
  14. 30
  15. 60
  16. 20
  17. 62
  18. 45
  19. 120
  20. 240
  21. 120
  22. 15
  23. 90
  24. 90
  25. 270
  26. 60
  27. 180
  28. 62
  29. 60
  30. 120
  31. 45
  32. 300
  33. 20
  34. 36
  35. 30
  36. 90
  37. 35
  38. 61
  39. 30
  40. 20

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