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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 205 · 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 250 litres and 300 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 6, 4 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.Two tanks hold 50 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  4. 4.Aarav takes 90 seconds and Kavya 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?
  5. 5.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 8, 10 or 3.
  6. 6.Three temple bells ring every 30, 20 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.Two tanks hold 150 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  8. 8.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?
  9. 9.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?
  10. 10.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?
  11. 11.Rahul takes 36 seconds and Kavya 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?
  12. 12.Three temple bells ring every 20, 6 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 5, 3 or 10.
  14. 14.Two tanks hold 20 litres and 25 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 160 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  16. 16.Three temple bells ring every 24, 8 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.Three temple bells ring every 5, 12 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 8, 6 or 3.
  19. 19.Two tanks hold 40 litres and 25 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  20. 20.Two tanks hold 100 litres and 250 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  21. 21.Ananya takes 72 seconds and Tara 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?
  22. 22.Three temple bells ring every 10, 20 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.Three temple bells ring every 5, 4 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.A hall floor is 175 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  25. 25.Three temple bells ring every 24, 10 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Two tanks hold 125 litres and 225 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 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 6, 4 or 15.
  29. 29.Three temple bells ring every 6, 15 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.Two tanks hold 180 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  31. 31.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 12, 4 or 15.
  32. 32.Two tanks hold 135 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  33. 33.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?
  34. 34.Three temple bells ring every 8, 6 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.Arjun takes 75 seconds and Rahul 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?
  36. 36.Three temple bells ring every 24, 5 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  37. 37.A hall floor is 300 cm long and 240 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  38. 38.Two tanks hold 30 litres and 105 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  39. 39.Rahul takes 80 seconds and Kabir 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?
  40. 40.Three temple bells ring every 20, 4 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 50
  2. 60
  3. 25
  4. 180
  5. 122
  6. 60
  7. 50
  8. 12
  9. 15
  10. 14
  11. 360
  12. 60
  13. 32
  14. 5
  15. 24
  16. 120
  17. 60
  18. 25
  19. 5
  20. 50
  21. 216
  22. 120
  23. 40
  24. 42
  25. 120
  26. 25
  27. 120
  28. 62
  29. 90
  30. 20
  31. 61
  32. 45
  33. 21
  34. 120
  35. 225
  36. 120
  37. 20
  38. 15
  39. 720
  40. 60

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