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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 64 · 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 270 cm long and 225 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  2. 2.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?
  3. 3.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 10, 15 or 5.
  4. 4.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?
  5. 5.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 8, 9 or 12.
  6. 6.A hall floor is 400 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  7. 7.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?
  8. 8.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?
  9. 9.Three temple bells ring every 9, 12 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.Find the smallest number bigger than 6 that leaves a remainder of 2 when divided by 4, 3 or 6.
  11. 11.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 8 or 3.
  12. 12.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 6, 9 or 3.
  13. 13.Three temple bells ring every 6, 9 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.A hall floor is 180 cm long and 135 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 18, 4 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.Two tanks hold 240 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  17. 17.Three temple bells ring every 6, 9 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.Three temple bells ring every 5, 4 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Two tanks hold 360 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  20. 20.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 4, 15 or 6.
  21. 21.A hall floor is 350 cm long and 300 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  22. 22.Two tanks hold 45 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  23. 23.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?
  24. 24.Meera takes 80 seconds and Farhan 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?
  25. 25.Aarav takes 45 seconds and Kavya 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?
  26. 26.Ananya takes 36 seconds and Diya 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?
  27. 27.Isha takes 90 seconds and Meera 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?
  28. 28.Two tanks hold 175 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  29. 29.Nisha takes 48 seconds and Vivaan 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?
  30. 30.Two tanks hold 20 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  31. 31.Two tanks hold 160 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  32. 32.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?
  33. 33.Three temple bells ring every 18, 30 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.Three temple bells ring every 12, 4 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.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?
  36. 36.Nisha takes 90 seconds and Zoya 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?
  37. 37.Two tanks hold 180 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  38. 38.Ananya takes 75 seconds and Aarav 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?
  39. 39.Three temple bells ring every 10, 12 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  40. 40.Farhan takes 60 seconds and Karan 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?

Answer key

  1. 30
  2. 42
  3. 32
  4. 20
  5. 73
  6. 24
  7. 50
  8. 120
  9. 72
  10. 14
  11. 26
  12. 20
  13. 72
  14. 12
  15. 72
  16. 40
  17. 90
  18. 20
  19. 40
  20. 61
  21. 42
  22. 15
  23. 21
  24. 400
  25. 225
  26. 180
  27. 450
  28. 25
  29. 144
  30. 5
  31. 20
  32. 15
  33. 90
  34. 60
  35. 40
  36. 450
  37. 20
  38. 300
  39. 120
  40. 180

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