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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 162 · 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 125 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  2. 2.Nisha takes 50 seconds and Meera 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?
  3. 3.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 8, 3 or 4.
  4. 4.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?
  5. 5.Two tanks hold 20 litres and 35 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  6. 6.Find the smallest number bigger than 6 that leaves a remainder of 2 when divided by 3, 4 or 6.
  7. 7.Three temple bells ring every 8, 6 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.Two tanks hold 105 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  9. 9.Two tanks hold 200 litres and 240 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  10. 10.Three temple bells ring every 10, 12 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.Isha takes 50 seconds and Meera 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?
  12. 12.Three temple bells ring every 24, 4 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.Three temple bells ring every 18, 9 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 3, 5 or 6.
  15. 15.Sneha takes 40 seconds and Priya 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?
  16. 16.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 5, 9 or 6.
  17. 17.A hall floor is 315 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  18. 18.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 10, 3 or 8.
  19. 19.Three temple bells ring every 30, 4 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.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?
  21. 21.Two tanks hold 120 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  22. 22.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?
  23. 23.Aarav takes 36 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?
  24. 24.A hall floor is 300 cm long and 250 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  25. 25.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 3, 5 or 8.
  26. 26.Tara takes 60 seconds and Manav 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?
  27. 27.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 3 or 6.
  28. 28.Arjun takes 48 seconds and Aditya takes 54 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?
  29. 29.Two tanks hold 210 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  30. 30.Three temple bells ring every 12, 18 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.Meera takes 50 seconds and Ananya 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?
  32. 32.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?
  33. 33.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 4 or 8.
  34. 34.Arjun takes 80 seconds and Aarav 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?
  35. 35.Three temple bells ring every 5, 15 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.Three temple bells ring every 30, 15 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  37. 37.Arjun takes 36 seconds and Kabir 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.Three temple bells ring every 9, 12 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.Two tanks hold 180 litres and 210 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  40. 40.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?

Answer key

  1. 25
  2. 400
  3. 25
  4. 14
  5. 5
  6. 14
  7. 72
  8. 15
  9. 40
  10. 60
  11. 300
  12. 120
  13. 90
  14. 31
  15. 360
  16. 92
  17. 14
  18. 122
  19. 60
  20. 12
  21. 15
  22. 45
  23. 180
  24. 30
  25. 121
  26. 180
  27. 14
  28. 432
  29. 30
  30. 72
  31. 450
  32. 24
  33. 122
  34. 240
  35. 45
  36. 120
  37. 180
  38. 36
  39. 30
  40. 21

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