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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 227 · 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).

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  1. 1.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?
  2. 2.A hall floor is 160 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  3. 3.Three temple bells ring every 6, 8 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.Three temple bells ring every 24, 12 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.A hall floor is 200 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  6. 6.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 3 or 10.
  7. 7.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 15, 5 or 10.
  8. 8.Two tanks hold 210 litres and 270 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  9. 9.Three temple bells ring every 6, 18 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.Zoya takes 45 seconds and Rahul 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?
  11. 11.Rahul takes 48 seconds and Saanvi 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?
  12. 12.Three temple bells ring every 18, 15 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.Rohan takes 45 seconds and Vivaan 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?
  14. 14.Three temple bells ring every 24, 20 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  15. 15.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 8 or 4.
  16. 16.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 8, 10 or 6.
  17. 17.Three temple bells ring every 5, 12 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.A hall floor is 135 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  19. 19.Kavya takes 45 seconds and Sneha 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?
  20. 20.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 5, 12 or 8.
  21. 21.A hall floor is 480 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  22. 22.Three temple bells ring every 6, 24 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.Three temple bells ring every 4, 24 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 6, 3 or 4.
  25. 25.Find the smallest number bigger than 6 that leaves a remainder of 2 when divided by 5, 6 or 4.
  26. 26.Three temple bells ring every 4, 8 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.Find the smallest number bigger than 6 that leaves a remainder of 2 when divided by 3, 6 or 5.
  28. 28.Two tanks hold 105 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  29. 29.Isha takes 54 seconds and Ananya 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?
  30. 30.A hall floor is 160 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  31. 31.Two tanks hold 45 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  32. 32.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 9, 10 or 5.
  33. 33.Dev takes 36 seconds and Sneha 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?
  34. 34.Three temple bells ring every 9, 15 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.Isha takes 72 seconds and Meera 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?
  36. 36.Three temple bells ring every 24, 6 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  37. 37.Three temple bells ring every 8, 6 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.Two tanks hold 150 litres and 240 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  39. 39.Three temple bells ring every 10, 12 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  40. 40.Three temple bells ring every 12, 20 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 60
  2. 24
  3. 120
  4. 120
  5. 15
  6. 62
  7. 33
  8. 30
  9. 72
  10. 450
  11. 240
  12. 90
  13. 720
  14. 120
  15. 25
  16. 122
  17. 60
  18. 6
  19. 450
  20. 123
  21. 24
  22. 72
  23. 120
  24. 13
  25. 62
  26. 40
  27. 32
  28. 15
  29. 432
  30. 40
  31. 15
  32. 92
  33. 720
  34. 90
  35. 360
  36. 120
  37. 72
  38. 30
  39. 60
  40. 60

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