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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 326 · 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 35 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  2. 2.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 3, 8 or 5.
  3. 3.Nisha takes 90 seconds and Farhan 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?
  4. 4.A hall floor is 140 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  5. 5.Three temple bells ring every 30, 5 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.A hall floor is 200 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  7. 7.Rohan takes 72 seconds and Karan 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?
  8. 8.Two tanks hold 120 litres and 320 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  9. 9.Three temple bells ring every 5, 6 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.A hall floor is 200 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  11. 11.Three temple bells ring every 30, 12 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.Two tanks hold 40 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  13. 13.Two tanks hold 200 litres and 175 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.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?
  15. 15.Three temple bells ring every 20, 4 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 20, 15 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.Two tanks hold 360 litres and 315 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  18. 18.Three temple bells ring every 20, 5 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Ananya takes 50 seconds and Zoya 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?
  20. 20.Priya takes 40 seconds and Tara 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?
  21. 21.Zoya takes 40 seconds and Tara 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?
  22. 22.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 4, 3 or 10.
  23. 23.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 12, 15 or 3.
  24. 24.Three temple bells ring every 5, 8 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.Two tanks hold 50 litres and 125 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  26. 26.Two tanks hold 135 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.A hall floor is 315 cm long and 135 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  28. 28.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 15, 9 or 4.
  29. 29.Three temple bells ring every 20, 4 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.Three temple bells ring every 6, 4 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.Three temple bells ring every 8, 6 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.Two tanks hold 100 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  33. 33.Three temple bells ring every 12, 20 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.A hall floor is 350 cm long and 250 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  35. 35.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 8 or 6.
  36. 36.Three temple bells ring every 6, 15 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  37. 37.A hall floor is 60 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  38. 38.Two tanks hold 120 litres and 160 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  39. 39.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 15, 10 or 8.
  40. 40.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 4 or 5.

Answer key

  1. 5
  2. 121
  3. 720
  4. 28
  5. 90
  6. 12
  7. 360
  8. 40
  9. 30
  10. 24
  11. 60
  12. 20
  13. 25
  14. 15
  15. 60
  16. 120
  17. 45
  18. 120
  19. 450
  20. 360
  21. 360
  22. 62
  23. 62
  24. 40
  25. 25
  26. 45
  27. 21
  28. 183
  29. 120
  30. 60
  31. 24
  32. 25
  33. 120
  34. 35
  35. 121
  36. 120
  37. 6
  38. 40
  39. 124
  40. 62

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