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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 361 · 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 405 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  2. 2.Two tanks hold 60 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  3. 3.Three temple bells ring every 10, 8 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.A hall floor is 250 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  5. 5.Arjun takes 80 seconds and Ishaan 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?
  6. 6.A hall floor is 240 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  7. 7.Two tanks hold 45 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  8. 8.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 6, 8 or 10.
  9. 9.Two tanks hold 250 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  10. 10.Two tanks hold 105 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  11. 11.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?
  12. 12.Three temple bells ring every 10, 15 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.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?
  14. 14.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 8, 10 or 3.
  15. 15.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?
  16. 16.Zoya takes 30 seconds and Farhan 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?
  17. 17.A hall floor is 280 cm long and 160 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 12 that leaves a remainder of 2 when divided by 12, 3 or 9.
  19. 19.Vivaan takes 54 seconds and Ananya 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?
  20. 20.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?
  21. 21.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?
  22. 22.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 8, 10 or 3.
  23. 23.Rahul takes 36 seconds and Dev 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?
  24. 24.Three temple bells ring every 12, 30 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.A hall floor is 200 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  26. 26.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?
  27. 27.A hall floor is 420 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  28. 28.Three temple bells ring every 8, 4 and 18 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 15 that leaves a remainder of 4 when divided by 5, 15 or 9.
  30. 30.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 9, 3 or 15.
  31. 31.Two tanks hold 120 litres and 135 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  32. 32.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 10, 3 or 6.
  33. 33.Tara takes 60 seconds and Meera 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?
  34. 34.Find the smallest number bigger than 9 that leaves a remainder of 5 when divided by 8, 9 or 6.
  35. 35.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?
  36. 36.A hall floor is 300 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  37. 37.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 12, 15 or 3.
  38. 38.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 9, 12 or 8.
  39. 39.Arjun takes 60 seconds and Isha 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?
  40. 40.Three temple bells ring every 10, 4 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 45
  2. 20
  3. 40
  4. 10
  5. 720
  6. 30
  7. 15
  8. 121
  9. 50
  10. 15
  11. 15
  12. 120
  13. 12
  14. 121
  15. 56
  16. 360
  17. 28
  18. 38
  19. 540
  20. 20
  21. 120
  22. 122
  23. 144
  24. 120
  25. 15
  26. 5
  27. 14
  28. 72
  29. 49
  30. 46
  31. 15
  32. 31
  33. 300
  34. 77
  35. 15
  36. 10
  37. 61
  38. 74
  39. 240
  40. 60

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