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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 76 · 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 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?
  2. 2.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?
  3. 3.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 9, 4 or 3.
  4. 4.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 5, 15 or 6.
  5. 5.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?
  6. 6.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 3, 6 or 9.
  7. 7.Three temple bells ring every 15, 9 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.Kavya takes 45 seconds and Farhan 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?
  9. 9.Kabir takes 72 seconds and Rahul 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?
  10. 10.A hall floor is 200 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  11. 11.A hall floor is 300 cm long and 180 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 5, 12 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.Farhan takes 72 seconds and Arjun 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?
  14. 14.Two tanks hold 315 litres and 135 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 30, 8 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.Pooja 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?
  17. 17.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?
  18. 18.Three temple bells ring every 18, 6 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Nisha takes 60 seconds and Meera 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.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 6, 8 or 9.
  21. 21.Dev takes 40 seconds and Rohan 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?
  22. 22.Karan takes 75 seconds and Pooja 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?
  23. 23.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 8, 5 or 4.
  24. 24.Two tanks hold 120 litres and 105 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  25. 25.A hall floor is 135 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  26. 26.Three temple bells ring every 24, 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 360 cm long and 300 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  28. 28.A hall floor is 140 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  29. 29.A hall floor is 320 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  30. 30.Two tanks hold 225 litres and 125 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 2 when divided by 3, 15 or 10.
  32. 32.A hall floor is 100 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  33. 33.Two tanks hold 400 litres and 350 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  34. 34.Pooja takes 30 seconds and Priya 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?
  35. 35.Three temple bells ring every 10, 24 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.Kavya takes 90 seconds and Karan 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?
  37. 37.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 10, 5 or 4.
  38. 38.Two tanks hold 80 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  39. 39.Aditya takes 30 seconds and Diya 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.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 9, 5 or 4.

Answer key

  1. 10
  2. 14
  3. 37
  4. 32
  5. 21
  6. 19
  7. 90
  8. 90
  9. 360
  10. 10
  11. 15
  12. 60
  13. 216
  14. 45
  15. 120
  16. 720
  17. 28
  18. 90
  19. 360
  20. 74
  21. 360
  22. 150
  23. 42
  24. 15
  25. 6
  26. 120
  27. 30
  28. 14
  29. 40
  30. 25
  31. 32
  32. 20
  33. 50
  34. 240
  35. 120
  36. 720
  37. 23
  38. 20
  39. 360
  40. 182

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