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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 519 · 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 90 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 12, 5 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.Manav takes 72 seconds and Arjun 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?
  4. 4.Three temple bells ring every 9, 24 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.Two tanks hold 100 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  6. 6.Three temple bells ring every 24, 10 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.A hall floor is 250 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  8. 8.Kabir takes 60 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?
  9. 9.Three temple bells ring every 4, 6 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.Two tanks hold 140 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  11. 11.Two tanks hold 50 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  12. 12.Two tanks hold 100 litres and 140 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  13. 13.A hall floor is 350 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  14. 14.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?
  15. 15.Three temple bells ring every 15, 20 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.Three temple bells ring every 30, 4 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 8, 3 or 12.
  18. 18.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?
  19. 19.Saanvi takes 54 seconds and Aditya 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?
  20. 20.Two tanks hold 45 litres and 60 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 30, 15 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.A hall floor is 480 cm long and 420 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  23. 23.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 3, 8 or 15.
  24. 24.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 10, 6 or 4.
  25. 25.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 3, 15 or 12.
  26. 26.Three temple bells ring every 8, 20 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.A hall floor is 100 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  28. 28.Two tanks hold 90 litres and 210 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  29. 29.Two tanks hold 90 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.Manav takes 30 seconds and Sneha 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?
  31. 31.A hall floor is 150 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  32. 32.Pooja takes 90 seconds and Dev 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?
  33. 33.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 8, 15 or 6.
  34. 34.Priya takes 54 seconds and Kabir 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?
  35. 35.Three temple bells ring every 24, 20 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.Find the smallest number bigger than 5 that leaves a remainder of 2 when divided by 3, 5 or 4.
  37. 37.Three temple bells ring every 5, 8 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.Three temple bells ring every 30, 12 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.A hall floor is 90 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  40. 40.Three temple bells ring every 24, 15 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 10
  2. 120
  3. 360
  4. 72
  5. 20
  6. 120
  7. 20
  8. 300
  9. 60
  10. 20
  11. 10
  12. 20
  13. 28
  14. 15
  15. 60
  16. 60
  17. 26
  18. 10
  19. 216
  20. 15
  21. 60
  22. 56
  23. 122
  24. 61
  25. 61
  26. 120
  27. 15
  28. 30
  29. 30
  30. 150
  31. 6
  32. 180
  33. 121
  34. 108
  35. 120
  36. 62
  37. 120
  38. 60
  39. 6
  40. 120

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