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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 269 · 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.A hall floor is 225 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  2. 2.Kavya takes 30 seconds and Ishaan 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?
  3. 3.Three temple bells ring every 18, 10 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.Three temple bells ring every 18, 4 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.Three temple bells ring every 15, 24 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.Three temple bells ring every 8, 15 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.Three temple bells ring every 4, 9 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 4 or 6.
  9. 9.Three temple bells ring every 15, 5 and 9 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 9 that leaves a remainder of 1 when divided by 6, 9 or 3.
  11. 11.Rahul takes 45 seconds and Manav 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?
  12. 12.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 6, 3 or 15.
  13. 13.A hall floor is 100 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  14. 14.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 3, 15 or 8.
  15. 15.Two tanks hold 45 litres and 60 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 120 litres and 320 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  17. 17.Three temple bells ring every 5, 6 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.Three temple bells ring every 12, 8 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Karan takes 36 seconds and Zoya 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?
  20. 20.A hall floor is 60 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  21. 21.Sneha takes 30 seconds and Manav 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?
  22. 22.Two tanks hold 15 litres and 10 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  23. 23.Two tanks hold 240 litres and 210 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 5, 18 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.A hall floor is 240 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  26. 26.Two tanks hold 125 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  27. 27.Find the smallest number bigger than 12 that leaves a remainder of 7 when divided by 8, 12 or 9.
  28. 28.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 6 or 3.
  29. 29.Three temple bells ring every 4, 18 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.Three temple bells ring every 30, 6 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.Kavya takes 45 seconds and Diya 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.A hall floor is 420 cm long and 240 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  33. 33.Three temple bells ring every 15, 10 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.Two tanks hold 400 litres and 150 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 8, 15 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.Three temple bells ring every 6, 20 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  37. 37.Tara takes 36 seconds and Meera 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?
  38. 38.Three temple bells ring every 10, 15 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.A hall floor is 400 cm long and 350 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  40. 40.Manav takes 72 seconds and Sneha 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. 10
  2. 120
  3. 90
  4. 36
  5. 120
  6. 120
  7. 36
  8. 14
  9. 45
  10. 19
  11. 225
  12. 31
  13. 10
  14. 121
  15. 15
  16. 40
  17. 60
  18. 120
  19. 144
  20. 6
  21. 180
  22. 5
  23. 30
  24. 90
  25. 12
  26. 25
  27. 79
  28. 32
  29. 72
  30. 60
  31. 180
  32. 28
  33. 120
  34. 50
  35. 120
  36. 120
  37. 144
  38. 60
  39. 56
  40. 360

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