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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 117 · 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 120 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  2. 2.Ananya takes 80 seconds and Pooja 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?
  3. 3.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?
  4. 4.Dev takes 54 seconds and Nisha 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?
  5. 5.Three temple bells ring every 10, 24 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.Three temple bells ring every 8, 9 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.Two tanks hold 280 litres and 160 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  8. 8.Ananya takes 48 seconds and Nisha 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.A hall floor is 280 cm long and 240 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  10. 10.A hall floor is 350 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  11. 11.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 9, 15 or 4.
  12. 12.Find the smallest number bigger than 15 that leaves a remainder of 5 when divided by 10, 8 or 15.
  13. 13.Three temple bells ring every 9, 30 and 15 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 8 that leaves a remainder of 2 when divided by 5, 4 or 8.
  15. 15.Three temple bells ring every 30, 9 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.A hall floor is 120 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  17. 17.Ananya takes 36 seconds and Priya 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?
  18. 18.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?
  19. 19.A hall floor is 360 cm long and 225 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  20. 20.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 12, 4 or 15.
  21. 21.Two tanks hold 200 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  22. 22.Three temple bells ring every 20, 15 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.Three temple bells ring every 20, 10 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 8, 12 or 3.
  25. 25.Three temple bells ring every 9, 8 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.A hall floor is 250 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  27. 27.Vivaan takes 30 seconds and Isha 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?
  28. 28.Three temple bells ring every 10, 20 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Three temple bells ring every 10, 4 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 5, 9 or 12.
  31. 31.A hall floor is 320 cm long and 280 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  32. 32.Two tanks hold 25 litres and 10 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  33. 33.Find the smallest number bigger than 6 that leaves a remainder of 2 when divided by 3, 6 or 5.
  34. 34.Three temple bells ring every 15, 6 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.A hall floor is 100 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  36. 36.Aarav takes 54 seconds and Kavya 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?
  37. 37.Three temple bells ring every 4, 15 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.A hall floor is 225 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  39. 39.Three temple bells ring every 20, 30 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  40. 40.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 10, 5 or 15.

Answer key

  1. 40
  2. 240
  3. 21
  4. 216
  5. 120
  6. 72
  7. 40
  8. 240
  9. 42
  10. 14
  11. 182
  12. 125
  13. 90
  14. 42
  15. 90
  16. 6
  17. 180
  18. 21
  19. 40
  20. 62
  21. 25
  22. 60
  23. 60
  24. 25
  25. 72
  26. 15
  27. 240
  28. 60
  29. 60
  30. 181
  31. 56
  32. 5
  33. 32
  34. 30
  35. 10
  36. 270
  37. 60
  38. 20
  39. 60
  40. 33

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