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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 126 · 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.Two tanks hold 175 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  2. 2.Three temple bells ring every 18, 12 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.A hall floor is 160 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  4. 4.A hall floor is 180 cm long and 135 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  5. 5.Dev takes 54 seconds and Ishaan 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?
  6. 6.Three temple bells ring every 12, 10 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.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?
  8. 8.A hall floor is 200 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  9. 9.Dev takes 90 seconds and Aarav 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?
  10. 10.Nisha takes 45 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?
  11. 11.Kavya takes 54 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?
  12. 12.Manav takes 90 seconds and Ananya 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?
  13. 13.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 6 or 3.
  14. 14.Two tanks hold 50 litres and 125 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  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 200 cm long and 175 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  17. 17.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 5, 9 or 15.
  18. 18.Ishaan takes 36 seconds and Diya 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?
  19. 19.Find the smallest number bigger than 15 that leaves a remainder of 9 when divided by 15, 10 or 12.
  20. 20.Three temple bells ring every 5, 24 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.A hall floor is 210 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  22. 22.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?
  23. 23.Three temple bells ring every 5, 6 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Three temple bells ring every 8, 20 and 15 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.Two tanks hold 210 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  27. 27.Two tanks hold 75 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  28. 28.Three temple bells ring every 6, 20 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Find the smallest number bigger than 12 that leaves a remainder of 7 when divided by 8, 9 or 12.
  30. 30.Three temple bells ring every 30, 4 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.Three temple bells ring every 9, 12 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.Two tanks hold 160 litres and 360 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  33. 33.Two tanks hold 90 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  34. 34.Three temple bells ring every 8, 6 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.Three temple bells ring every 30, 24 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.Three temple bells ring every 24, 15 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 8 that leaves a remainder of 2 when divided by 4, 8 or 3.
  38. 38.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?
  39. 39.Two tanks hold 150 litres and 350 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  40. 40.Three temple bells ring every 8, 5 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 25
  2. 72
  3. 40
  4. 12
  5. 270
  6. 60
  7. 15
  8. 24
  9. 450
  10. 720
  11. 216
  12. 450
  13. 31
  14. 25
  15. 12
  16. 56
  17. 49
  18. 180
  19. 69
  20. 120
  21. 28
  22. 50
  23. 60
  24. 120
  25. 10
  26. 30
  27. 15
  28. 60
  29. 79
  30. 120
  31. 72
  32. 40
  33. 10
  34. 120
  35. 120
  36. 120
  37. 26
  38. 35
  39. 50
  40. 120

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