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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 470 · 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 6, 5 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.A hall floor is 480 cm long and 300 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 30, 10 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.A hall floor is 100 cm long and 80 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 12 that leaves a remainder of 3 when divided by 12, 8 or 10.
  6. 6.Two tanks hold 15 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  7. 7.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?
  8. 8.Three temple bells ring every 6, 15 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.Diya takes 90 seconds and Tara 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?
  10. 10.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?
  11. 11.Two tanks hold 40 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  12. 12.Pooja takes 45 seconds and Manav 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?
  13. 13.Vivaan takes 48 seconds and Pooja 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.A hall floor is 360 cm long and 225 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  15. 15.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 5, 8 or 10.
  16. 16.Two tanks hold 280 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  17. 17.Three temple bells ring every 30, 8 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.Three temple bells ring every 6, 4 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Rohan takes 90 seconds and Vivaan 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?
  20. 20.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 9, 10 or 3.
  21. 21.A hall floor is 300 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  22. 22.Find the smallest number bigger than 8 that leaves a remainder of 4 when divided by 5, 8 or 6.
  23. 23.Arjun takes 60 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?
  24. 24.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?
  25. 25.Two tanks hold 360 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  26. 26.Two tanks hold 225 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  27. 27.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 4, 3 or 12.
  28. 28.Two tanks hold 30 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.Three temple bells ring every 30, 6 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.Three temple bells ring every 10, 6 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.Two tanks hold 400 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  32. 32.Three temple bells ring every 8, 6 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.Three temple bells ring every 15, 10 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.Two tanks hold 30 litres and 25 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  35. 35.Three temple bells ring every 18, 30 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.Two tanks hold 120 litres and 280 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  37. 37.Aarav takes 80 seconds and Rahul 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?
  38. 38.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 4 or 8.
  39. 39.Two tanks hold 100 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  40. 40.Farhan takes 72 seconds and Meera 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. 30
  2. 40
  3. 90
  4. 20
  5. 123
  6. 5
  7. 15
  8. 30
  9. 450
  10. 14
  11. 5
  12. 90
  13. 720
  14. 40
  15. 43
  16. 40
  17. 120
  18. 24
  19. 360
  20. 91
  21. 10
  22. 124
  23. 240
  24. 40
  25. 40
  26. 25
  27. 13
  28. 10
  29. 60
  30. 60
  31. 50
  32. 72
  33. 90
  34. 5
  35. 90
  36. 40
  37. 720
  38. 121
  39. 25
  40. 360

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