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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 504 · 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 45 litres and 60 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.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?
  4. 4.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 8, 6 or 12.
  5. 5.A hall floor is 280 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  6. 6.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?
  7. 7.Find the smallest number bigger than 5 that leaves a remainder of 2 when divided by 3, 4 or 5.
  8. 8.Aarav takes 54 seconds and Ishaan 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?
  9. 9.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 8 or 4.
  10. 10.A hall floor is 75 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  11. 11.Two tanks hold 105 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  12. 12.A hall floor is 420 cm long and 300 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  13. 13.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?
  14. 14.Two tanks hold 140 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  15. 15.A hall floor is 420 cm long and 240 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  16. 16.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?
  17. 17.Two tanks hold 35 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  18. 18.Nisha takes 75 seconds and Meera 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?
  19. 19.A hall floor is 280 cm long and 160 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  20. 20.A hall floor is 180 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  21. 21.Pooja takes 72 seconds and Sneha 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?
  22. 22.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 6 or 4.
  23. 23.Diya takes 45 seconds and Kabir 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?
  24. 24.Find the smallest number bigger than 6 that leaves a remainder of 3 when divided by 4, 5 or 6.
  25. 25.Three temple bells ring every 15, 12 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.A hall floor is 420 cm long and 360 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  27. 27.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 12, 10 or 9.
  28. 28.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 4, 9 or 10.
  29. 29.Two tanks hold 280 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  30. 30.Two tanks hold 180 litres and 140 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  31. 31.Farhan takes 60 seconds and Isha 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?
  32. 32.Two tanks hold 80 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  33. 33.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?
  34. 34.Arjun takes 60 seconds and Farhan 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?
  35. 35.Two tanks hold 45 litres and 10 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  36. 36.Three temple bells ring every 15, 20 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  37. 37.Three temple bells ring every 24, 12 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.Three temple bells ring every 30, 4 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.Find the smallest number bigger than 12 that leaves a remainder of 4 when divided by 8, 12 or 6.
  40. 40.Three temple bells ring every 10, 6 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 15
  2. 14
  3. 30
  4. 27
  5. 35
  6. 60
  7. 62
  8. 540
  9. 121
  10. 6
  11. 15
  12. 35
  13. 56
  14. 20
  15. 28
  16. 90
  17. 5
  18. 300
  19. 28
  20. 6
  21. 144
  22. 62
  23. 225
  24. 63
  25. 60
  26. 42
  27. 183
  28. 181
  29. 40
  30. 20
  31. 120
  32. 40
  33. 42
  34. 180
  35. 5
  36. 60
  37. 120
  38. 60
  39. 28
  40. 30

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