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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 28 · 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.Isha takes 45 seconds and Tara 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?
  2. 2.Aarav takes 60 seconds and Nisha 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?
  3. 3.Three temple bells ring every 20, 15 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.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?
  5. 5.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 3, 5 or 10.
  6. 6.A hall floor is 175 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  7. 7.Two tanks hold 350 litres and 250 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  8. 8.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 6, 12 or 4.
  9. 9.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 12, 9 or 4.
  10. 10.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?
  11. 11.Three temple bells ring every 8, 5 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.Aditya takes 36 seconds and Manav 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?
  13. 13.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 9, 10 or 15.
  14. 14.A hall floor is 150 cm long and 125 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  15. 15.A hall floor is 350 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  16. 16.Kabir takes 30 seconds and Aarav 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?
  17. 17.Dev takes 45 seconds and Arjun 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?
  18. 18.Arjun takes 50 seconds and Aditya 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 2 when divided by 10, 4 or 15.
  20. 20.Two tanks hold 180 litres and 40 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 405 litres and 315 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 400 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  23. 23.Three temple bells ring every 9, 30 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Three temple bells ring every 24, 12 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.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?
  26. 26.Three temple bells ring every 20, 24 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.Two tanks hold 180 litres and 160 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  28. 28.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 9, 6 or 3.
  29. 29.A hall floor is 210 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  30. 30.Three temple bells ring every 15, 12 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.A hall floor is 125 cm long and 75 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 8 that leaves a remainder of 1 when divided by 6, 8 or 3.
  33. 33.Pooja takes 40 seconds and Rahul 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?
  34. 34.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 10, 15 or 12.
  35. 35.A hall floor is 225 cm long and 135 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  36. 36.Three temple bells ring every 30, 20 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  37. 37.Three temple bells ring every 18, 24 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.Karan takes 80 seconds and Rahul 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?
  39. 39.Three temple bells ring every 15, 10 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  40. 40.Three temple bells ring every 20, 30 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 360
  2. 360
  3. 120
  4. 6
  5. 32
  6. 28
  7. 50
  8. 15
  9. 39
  10. 15
  11. 120
  12. 144
  13. 92
  14. 30
  15. 28
  16. 120
  17. 270
  18. 150
  19. 62
  20. 20
  21. 45
  22. 24
  23. 90
  24. 72
  25. 10
  26. 120
  27. 20
  28. 19
  29. 35
  30. 60
  31. 15
  32. 25
  33. 120
  34. 62
  35. 15
  36. 60
  37. 72
  38. 720
  39. 120
  40. 60

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