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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 440 · 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 40 litres and 30 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 9 that leaves a remainder of 3 when divided by 4, 6 or 9.
  3. 3.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 6, 9 or 8.
  4. 4.Two tanks hold 40 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  5. 5.Three temple bells ring every 6, 30 and 20 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, 6 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.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?
  8. 8.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 10, 8 or 6.
  9. 9.A hall floor is 240 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  10. 10.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?
  11. 11.Three temple bells ring every 15, 4 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.Kabir takes 75 seconds and Vivaan 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?
  13. 13.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 3 or 10.
  14. 14.Three temple bells ring every 30, 12 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  15. 15.Priya takes 80 seconds and Ishaan 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?
  16. 16.Two tanks hold 75 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  17. 17.Karan takes 30 seconds and Sneha 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?
  18. 18.Isha takes 30 seconds and Nisha 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?
  19. 19.A hall floor is 315 cm long and 270 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  20. 20.Karan takes 50 seconds and Farhan 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?
  21. 21.Three temple bells ring every 20, 4 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Two tanks hold 180 litres and 135 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  23. 23.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 4, 12 or 6.
  24. 24.A hall floor is 210 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  25. 25.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 10, 6 or 9.
  26. 26.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 4, 15 or 10.
  27. 27.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 3, 9 or 6.
  28. 28.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 5, 8 or 12.
  29. 29.Three temple bells ring every 18, 30 and 15 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 15 that leaves a remainder of 2 when divided by 15, 5 or 12.
  31. 31.Diya takes 50 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?
  32. 32.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 10 or 4.
  33. 33.Farhan takes 45 seconds and Rohan takes 54 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?
  34. 34.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 3, 6 or 15.
  35. 35.Three temple bells ring every 9, 24 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.Two tanks hold 280 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  37. 37.Sneha takes 30 seconds and Ananya 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?
  38. 38.Two tanks hold 35 litres and 10 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  39. 39.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?
  40. 40.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?

Answer key

  1. 10
  2. 39
  3. 73
  4. 20
  5. 60
  6. 120
  7. 12
  8. 121
  9. 12
  10. 20
  11. 120
  12. 150
  13. 62
  14. 60
  15. 240
  16. 25
  17. 90
  18. 150
  19. 42
  20. 150
  21. 60
  22. 45
  23. 15
  24. 28
  25. 92
  26. 62
  27. 20
  28. 122
  29. 90
  30. 62
  31. 150
  32. 61
  33. 270
  34. 31
  35. 72
  36. 40
  37. 120
  38. 5
  39. 24
  40. 10

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