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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 316 · 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 8, 24 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.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?
  3. 3.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 10 or 4.
  4. 4.Three temple bells ring every 5, 8 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.A hall floor is 400 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  6. 6.Three temple bells ring every 6, 18 and 8 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 12 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, 30 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.Aarav takes 40 seconds and Meera 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?
  10. 10.Three temple bells ring every 8, 6 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.Three temple bells ring every 4, 10 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.Three temple bells ring every 20, 6 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.Three temple bells ring every 6, 8 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.A hall floor is 80 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  15. 15.Three temple bells ring every 5, 15 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.Two tanks hold 225 litres and 315 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 8 that leaves a remainder of 2 when divided by 4, 6 or 8.
  18. 18.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?
  19. 19.Rohan takes 48 seconds and Sneha 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?
  20. 20.Two tanks hold 210 litres and 240 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  21. 21.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?
  22. 22.A hall floor is 420 cm long and 300 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  23. 23.Zoya takes 40 seconds and Diya 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?
  24. 24.Two tanks hold 135 litres and 360 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  25. 25.Three temple bells ring every 24, 6 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.A hall floor is 175 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  27. 27.Arjun takes 72 seconds and Aarav 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?
  28. 28.Two tanks hold 80 litres and 70 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  29. 29.Aarav takes 48 seconds and Karan 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?
  30. 30.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 5 or 12.
  31. 31.Nisha takes 30 seconds and Karan 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?
  32. 32.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 6, 15 or 5.
  33. 33.Three temple bells ring every 20, 15 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.A hall floor is 350 cm long and 250 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  35. 35.Three temple bells ring every 18, 10 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 9, 10 or 3.
  37. 37.Two tanks hold 80 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  38. 38.Two tanks hold 350 litres and 300 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  39. 39.A hall floor is 175 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  40. 40.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?

Answer key

  1. 120
  2. 56
  3. 61
  4. 120
  5. 24
  6. 72
  7. 36
  8. 90
  9. 360
  10. 120
  11. 60
  12. 60
  13. 72
  14. 12
  15. 45
  16. 45
  17. 26
  18. 15
  19. 240
  20. 30
  21. 5
  22. 35
  23. 360
  24. 45
  25. 120
  26. 14
  27. 360
  28. 10
  29. 240
  30. 61
  31. 360
  32. 31
  33. 60
  34. 35
  35. 90
  36. 91
  37. 20
  38. 50
  39. 42
  40. 24

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