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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 186 · 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 20, 24 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 240 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  3. 3.Two tanks hold 150 litres and 240 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  4. 4.Find the smallest number bigger than 12 that leaves a remainder of 4 when divided by 10, 12 or 6.
  5. 5.Three temple bells ring every 6, 8 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 5 or 8.
  7. 7.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 3 or 10.
  8. 8.Aditya takes 36 seconds and Zoya 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?
  9. 9.Two tanks hold 360 litres and 135 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  10. 10.A hall floor is 240 cm long and 210 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  11. 11.Two tanks hold 75 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.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?
  13. 13.Three temple bells ring every 12, 15 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.Three temple bells ring every 5, 24 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  15. 15.Kavya takes 60 seconds and Arjun 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?
  16. 16.Three temple bells ring every 9, 24 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 4 or 10.
  18. 18.Three temple bells ring every 24, 15 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 6, 15 or 3.
  20. 20.Vivaan takes 45 seconds and Arjun 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?
  21. 21.Three temple bells ring every 30, 9 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Find the smallest number bigger than 9 that leaves a remainder of 3 when divided by 4, 9 or 6.
  23. 23.Two tanks hold 20 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  24. 24.Three temple bells ring every 18, 6 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.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?
  26. 26.Kavya takes 80 seconds and Manav 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?
  27. 27.Two tanks hold 35 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.A hall floor is 200 cm long and 150 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 1 when divided by 5, 3 or 10.
  30. 30.Aditya takes 45 seconds and Rohan 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?
  31. 31.Two tanks hold 10 litres and 15 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  32. 32.A hall floor is 210 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  33. 33.Arjun takes 40 seconds and Aditya 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?
  34. 34.Two tanks hold 450 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  35. 35.Two tanks hold 200 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  36. 36.Pooja takes 45 seconds and Dev 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?
  37. 37.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 4, 3 or 12.
  38. 38.A hall floor is 315 cm long and 135 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  39. 39.Three temple bells ring every 20, 12 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  40. 40.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?

Answer key

  1. 120
  2. 24
  3. 30
  4. 64
  5. 24
  6. 121
  7. 62
  8. 360
  9. 45
  10. 56
  11. 15
  12. 30
  13. 60
  14. 120
  15. 120
  16. 72
  17. 61
  18. 120
  19. 31
  20. 720
  21. 90
  22. 39
  23. 10
  24. 90
  25. 56
  26. 720
  27. 5
  28. 12
  29. 31
  30. 450
  31. 5
  32. 14
  33. 360
  34. 50
  35. 40
  36. 225
  37. 13
  38. 21
  39. 120
  40. 40

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