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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 240 · 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 12 that leaves a remainder of 2 when divided by 9, 12 or 3.
  2. 2.Three temple bells ring every 4, 9 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.Kabir takes 54 seconds and Dev 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 10, 5 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.Two tanks hold 30 litres and 25 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  6. 6.Two tanks hold 45 litres and 105 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  7. 7.Three temple bells ring every 30, 12 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.Three temple bells ring every 18, 10 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.Three temple bells ring every 6, 18 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.A hall floor is 125 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  11. 11.Three temple bells ring every 24, 9 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.Three temple bells ring every 15, 6 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.Meera takes 30 seconds and Karan 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?
  14. 14.Two tanks hold 100 litres and 75 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 15, 9 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.Three temple bells ring every 6, 8 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.Pooja takes 48 seconds and Vivaan 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?
  18. 18.Three temple bells ring every 9, 5 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Two tanks hold 225 litres and 360 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  20. 20.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 10, 8 or 5.
  21. 21.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 10, 5 or 15.
  22. 22.Zoya takes 48 seconds and Kabir 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?
  23. 23.Three temple bells ring every 4, 30 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Three temple bells ring every 4, 6 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.Three temple bells ring every 30, 6 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 10, 12 or 5.
  27. 27.Kavya takes 54 seconds and Aditya 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?
  28. 28.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 3 or 6.
  29. 29.Three temple bells ring every 15, 4 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.A hall floor is 420 cm long and 360 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  31. 31.Ananya takes 45 seconds and Manav 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?
  32. 32.Two tanks hold 30 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  33. 33.Three temple bells ring every 20, 24 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.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?
  35. 35.A hall floor is 320 cm long and 280 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  36. 36.Sneha takes 54 seconds and Tara 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.Three temple bells ring every 12, 30 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.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?
  39. 39.A hall floor is 250 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  40. 40.Rohan takes 40 seconds and Kavya 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?

Answer key

  1. 38
  2. 36
  3. 270
  4. 40
  5. 5
  6. 15
  7. 60
  8. 90
  9. 36
  10. 10
  11. 72
  12. 120
  13. 270
  14. 25
  15. 90
  16. 120
  17. 240
  18. 90
  19. 45
  20. 42
  21. 32
  22. 144
  23. 120
  24. 60
  25. 90
  26. 61
  27. 216
  28. 32
  29. 60
  30. 42
  31. 180
  32. 10
  33. 120
  34. 90
  35. 56
  36. 270
  37. 60
  38. 120
  39. 15
  40. 360

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