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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 551 · 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.A hall floor is 120 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  2. 2.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 3, 5 or 15.
  3. 3.Two tanks hold 30 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  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.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 10 or 4.
  6. 6.A hall floor is 140 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  7. 7.Two tanks hold 60 litres and 70 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  8. 8.Two tanks hold 90 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  9. 9.Isha takes 40 seconds and Ananya 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?
  10. 10.Two tanks hold 250 litres and 350 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 175 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  12. 12.Aarav takes 30 seconds and Tara 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?
  13. 13.Three temple bells ring every 15, 12 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.Three temple bells ring every 12, 5 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  15. 15.Two tanks hold 150 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  16. 16.Three temple bells ring every 6, 4 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.A hall floor is 360 cm long and 135 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 20, 6 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Three temple bells ring every 6, 15 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 9, 8 or 3.
  21. 21.Two tanks hold 75 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  22. 22.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?
  23. 23.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 3 or 4.
  24. 24.Two tanks hold 40 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  25. 25.Three temple bells ring every 6, 10 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Three temple bells ring every 9, 6 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.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?
  28. 28.Two tanks hold 180 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  29. 29.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 3 or 9.
  30. 30.Tara takes 45 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?
  31. 31.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?
  32. 32.Three temple bells ring every 12, 5 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 6, 8 or 3.
  34. 34.A hall floor is 315 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  35. 35.A hall floor is 150 cm long and 125 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  36. 36.A hall floor is 80 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  37. 37.Two tanks hold 90 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  38. 38.Three temple bells ring every 18, 8 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.Kabir takes 50 seconds and Nisha takes 40 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 12, 30 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 30
  2. 16
  3. 15
  4. 28
  5. 62
  6. 35
  7. 10
  8. 10
  9. 360
  10. 50
  11. 21
  12. 150
  13. 60
  14. 120
  15. 30
  16. 60
  17. 24
  18. 60
  19. 90
  20. 74
  21. 15
  22. 15
  23. 61
  24. 10
  25. 30
  26. 72
  27. 90
  28. 20
  29. 47
  30. 90
  31. 120
  32. 60
  33. 25
  34. 28
  35. 30
  36. 12
  37. 45
  38. 72
  39. 200
  40. 60

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