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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 477 · 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.Kabir takes 30 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?
  2. 2.Two tanks hold 360 litres and 405 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  3. 3.Diya takes 75 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?
  4. 4.Three temple bells ring every 24, 8 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.A hall floor is 210 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  6. 6.Nisha takes 50 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?
  7. 7.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 6, 10 or 4.
  8. 8.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?
  9. 9.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 5, 9 or 12.
  10. 10.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?
  11. 11.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?
  12. 12.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 12, 15 or 8.
  13. 13.Two tanks hold 45 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 4, 6 or 10.
  15. 15.A hall floor is 100 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  16. 16.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?
  17. 17.Two tanks hold 60 litres and 140 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  18. 18.Three temple bells ring every 4, 15 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.A hall floor is 270 cm long and 225 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  20. 20.Find the smallest number bigger than 8 that leaves a remainder of 3 when divided by 6, 8 or 5.
  21. 21.Rohan takes 50 seconds and Pooja 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?
  22. 22.Two tanks hold 350 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  23. 23.Three temple bells ring every 12, 20 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Two tanks hold 75 litres and 60 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 5, 8 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Kabir takes 45 seconds and Rahul 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?
  27. 27.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?
  28. 28.Two tanks hold 100 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  29. 29.Two tanks hold 360 litres and 160 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  30. 30.Three temple bells ring every 4, 9 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 4, 6 or 3.
  32. 32.A hall floor is 200 cm long and 125 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  33. 33.A hall floor is 150 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  34. 34.Aarav takes 60 seconds and Saanvi 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?
  35. 35.Two tanks hold 405 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  36. 36.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?
  37. 37.Three temple bells ring every 4, 10 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.Two tanks hold 270 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 12, 8 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  40. 40.Zoya takes 80 seconds and Diya takes 90 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. 150
  2. 45
  3. 150
  4. 120
  5. 21
  6. 200
  7. 62
  8. 24
  9. 183
  10. 10
  11. 15
  12. 123
  13. 15
  14. 62
  15. 12
  16. 35
  17. 20
  18. 120
  19. 30
  20. 123
  21. 150
  22. 50
  23. 60
  24. 15
  25. 40
  26. 360
  27. 20
  28. 20
  29. 40
  30. 72
  31. 13
  32. 40
  33. 15
  34. 180
  35. 45
  36. 21
  37. 40
  38. 30
  39. 72
  40. 720

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