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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 371 · 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 175 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  2. 2.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?
  3. 3.A hall floor is 150 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  4. 4.Ananya takes 54 seconds and Priya 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?
  5. 5.Sneha takes 75 seconds and Ananya 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?
  6. 6.Pooja takes 54 seconds and Aditya 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?
  7. 7.Three temple bells ring every 8, 4 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.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?
  9. 9.Kabir takes 36 seconds and Kavya 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?
  10. 10.Find the smallest number bigger than 12 that leaves a remainder of 4 when divided by 6, 9 or 12.
  11. 11.Karan takes 75 seconds and Pooja 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.Two tanks hold 45 litres and 10 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  13. 13.Aarav takes 40 seconds and Priya 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?
  14. 14.Three temple bells ring every 8, 18 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  15. 15.Aditya takes 72 seconds and Ishaan 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?
  16. 16.Two tanks hold 200 litres and 125 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  17. 17.A hall floor is 200 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  18. 18.Arjun takes 40 seconds and Farhan 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?
  19. 19.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 3, 15 or 4.
  20. 20.A hall floor is 420 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  21. 21.Three temple bells ring every 10, 6 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Three temple bells ring every 24, 5 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 5, 4 or 8.
  24. 24.Isha takes 40 seconds and Aditya 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?
  25. 25.Two tanks hold 30 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  26. 26.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 12 or 10.
  27. 27.Three temple bells ring every 8, 10 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.A hall floor is 480 cm long and 420 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  29. 29.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 9, 10 or 5.
  30. 30.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 4, 8 or 12.
  31. 31.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?
  32. 32.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 9, 3 or 10.
  33. 33.Two tanks hold 150 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  34. 34.Three temple bells ring every 8, 18 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.Three temple bells ring every 6, 24 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.Dev takes 60 seconds and Rohan 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?
  37. 37.Three temple bells ring every 20, 10 and 6 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 350 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  39. 39.Aarav takes 40 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?
  40. 40.Three temple bells ring every 15, 6 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 21
  2. 6
  3. 10
  4. 432
  5. 300
  6. 108
  7. 40
  8. 60
  9. 144
  10. 40
  11. 600
  12. 5
  13. 360
  14. 72
  15. 360
  16. 25
  17. 10
  18. 600
  19. 61
  20. 14
  21. 90
  22. 120
  23. 41
  24. 120
  25. 15
  26. 62
  27. 120
  28. 56
  29. 93
  30. 26
  31. 42
  32. 91
  33. 50
  34. 72
  35. 120
  36. 240
  37. 60
  38. 50
  39. 360
  40. 60

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