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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 200 · 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.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?
  2. 2.Three temple bells ring every 9, 30 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.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?
  4. 4.Two tanks hold 120 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  5. 5.Three temple bells ring every 4, 10 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.Two tanks hold 105 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  7. 7.Two tanks hold 30 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  8. 8.Rohan takes 60 seconds and Arjun 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?
  9. 9.A hall floor is 140 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  10. 10.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?
  11. 11.A hall floor is 315 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  12. 12.Aarav takes 48 seconds and Kabir 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?
  13. 13.Three temple bells ring every 15, 8 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.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?
  15. 15.A hall floor is 60 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  16. 16.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?
  17. 17.Three temple bells ring every 24, 4 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.Diya takes 75 seconds and Kavya 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?
  19. 19.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 10, 3 or 9.
  20. 20.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?
  21. 21.Three temple bells ring every 6, 24 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Meera takes 90 seconds and Diya 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?
  23. 23.Priya takes 40 seconds and Kavya 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?
  24. 24.Zoya takes 40 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?
  25. 25.Two tanks hold 80 litres and 280 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 20 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  27. 27.Three temple bells ring every 12, 10 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.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?
  29. 29.Pooja takes 75 seconds and Diya 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?
  30. 30.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 12, 10 or 15.
  31. 31.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 9, 6 or 12.
  32. 32.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 6, 9 or 3.
  33. 33.Nisha 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?
  34. 34.Find the smallest number bigger than 12 that leaves a remainder of 4 when divided by 12, 5 or 10.
  35. 35.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?
  36. 36.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?
  37. 37.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 4, 8 or 10.
  38. 38.Three temple bells ring every 5, 18 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 9, 3 or 10.
  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. 21
  2. 90
  3. 30
  4. 30
  5. 60
  6. 15
  7. 10
  8. 360
  9. 21
  10. 10
  11. 28
  12. 240
  13. 120
  14. 60
  15. 6
  16. 14
  17. 120
  18. 150
  19. 91
  20. 25
  21. 120
  22. 450
  23. 360
  24. 120
  25. 40
  26. 10
  27. 60
  28. 30
  29. 150
  30. 62
  31. 37
  32. 19
  33. 225
  34. 64
  35. 15
  36. 60
  37. 43
  38. 90
  39. 91
  40. 40

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