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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 7 · 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 90 litres and 70 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  2. 2.Three temple bells ring every 8, 5 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.Diya takes 60 seconds and Rohan 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?
  4. 4.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?
  5. 5.Three temple bells ring every 6, 12 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.Find the smallest number bigger than 10 that leaves a remainder of 4 when divided by 9, 10 or 5.
  7. 7.Three temple bells ring every 15, 4 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.Two tanks hold 100 litres and 350 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  9. 9.Sneha takes 40 seconds and Vivaan 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?
  10. 10.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 9, 6 or 12.
  11. 11.Find the smallest number bigger than 9 that leaves a remainder of 3 when divided by 9, 4 or 8.
  12. 12.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 4, 5 or 12.
  13. 13.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?
  14. 14.Two tanks hold 225 litres and 315 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  15. 15.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 8 or 6.
  16. 16.Find the smallest number bigger than 8 that leaves a remainder of 3 when divided by 8, 4 or 5.
  17. 17.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?
  18. 18.Three temple bells ring every 15, 20 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.A hall floor is 120 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  20. 20.Three temple bells ring every 8, 24 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.Find the smallest number bigger than 10 that leaves a remainder of 5 when divided by 10, 6 or 9.
  22. 22.Three temple bells ring every 8, 9 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.Pooja takes 40 seconds and Tara takes 90 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.Three temple bells ring every 30, 18 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.Three temple bells ring every 5, 12 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Pooja takes 40 seconds and Zoya 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?
  27. 27.Two tanks hold 400 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  28. 28.Three temple bells ring every 5, 8 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.A hall floor is 160 cm long and 140 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  30. 30.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 10, 6 or 4.
  31. 31.Three temple bells ring every 12, 24 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.A hall floor is 175 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  33. 33.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 3, 8 or 4.
  34. 34.Three temple bells ring every 5, 15 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 6, 15 or 4.
  36. 36.Two tanks hold 135 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  37. 37.Three temple bells ring every 8, 24 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 6, 8 or 5.
  39. 39.A hall floor is 160 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  40. 40.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 6 or 9.

Answer key

  1. 10
  2. 40
  3. 300
  4. 42
  5. 60
  6. 94
  7. 60
  8. 50
  9. 240
  10. 38
  11. 75
  12. 62
  13. 15
  14. 45
  15. 122
  16. 43
  17. 35
  18. 60
  19. 12
  20. 72
  21. 95
  22. 72
  23. 360
  24. 90
  25. 60
  26. 360
  27. 50
  28. 120
  29. 56
  30. 62
  31. 120
  32. 28
  33. 26
  34. 60
  35. 61
  36. 45
  37. 72
  38. 121
  39. 12
  40. 91

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