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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 426 · 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 20 litres and 70 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 5, 6 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.Two tanks hold 35 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  4. 4.Three temple bells ring every 24, 6 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.A hall floor is 350 cm long and 300 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  6. 6.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 3, 15 or 8.
  7. 7.Nisha takes 48 seconds and Ishaan 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?
  8. 8.A hall floor is 175 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  9. 9.Three temple bells ring every 12, 24 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.A hall floor is 180 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  11. 11.Three temple bells ring every 5, 4 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.A hall floor is 350 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  13. 13.Two tanks hold 175 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.Two tanks hold 280 litres and 240 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  15. 15.Three temple bells ring every 10, 5 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.Three temple bells ring every 10, 12 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.Aarav takes 45 seconds and Aditya 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?
  18. 18.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 5 or 6.
  19. 19.Two tanks hold 200 litres and 280 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  20. 20.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 6 or 3.
  21. 21.Two tanks hold 250 litres and 350 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  22. 22.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?
  23. 23.Three temple bells ring every 12, 4 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Three temple bells ring every 24, 20 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.Two tanks hold 140 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  26. 26.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 8, 4 or 10.
  27. 27.A hall floor is 420 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  28. 28.Find the smallest number bigger than 12 that leaves a remainder of 5 when divided by 12, 8 or 9.
  29. 29.Three temple bells ring every 24, 20 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.Three temple bells ring every 12, 15 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.Three temple bells ring every 30, 24 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 3, 6 or 12.
  33. 33.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 4, 5 or 8.
  34. 34.Two tanks hold 200 litres and 360 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 450 litres and 350 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  36. 36.Find the smallest number bigger than 5 that leaves a remainder of 1 when divided by 4, 3 or 5.
  37. 37.Isha takes 48 seconds and Diya 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?
  38. 38.Three temple bells ring every 4, 6 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.Two tanks hold 50 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  40. 40.Ishaan takes 54 seconds and Kabir 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?

Answer key

  1. 10
  2. 90
  3. 5
  4. 120
  5. 42
  6. 122
  7. 720
  8. 28
  9. 120
  10. 6
  11. 120
  12. 14
  13. 25
  14. 40
  15. 90
  16. 60
  17. 450
  18. 32
  19. 40
  20. 14
  21. 50
  22. 21
  23. 60
  24. 120
  25. 20
  26. 41
  27. 21
  28. 77
  29. 120
  30. 60
  31. 120
  32. 13
  33. 42
  34. 40
  35. 50
  36. 61
  37. 240
  38. 60
  39. 10
  40. 270

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