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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 203 · 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 135 litres and 315 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 10 that leaves a remainder of 4 when divided by 6, 10 or 5.
  3. 3.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?
  4. 4.Kabir 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?
  5. 5.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?
  6. 6.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 9, 5 or 10.
  7. 7.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 12, 4 or 9.
  8. 8.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?
  9. 9.A hall floor is 280 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  10. 10.Three temple bells ring every 8, 9 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.Tara takes 45 seconds and Dev 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?
  12. 12.Three temple bells ring every 12, 24 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.Three temple bells ring every 6, 12 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 4, 8 or 15.
  15. 15.Two tanks hold 200 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  16. 16.Zoya takes 45 seconds and Aarav 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?
  17. 17.Karan takes 30 seconds and Vivaan 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.Find the smallest number bigger than 6 that leaves a remainder of 2 when divided by 4, 3 or 6.
  19. 19.Find the smallest number bigger than 9 that leaves a remainder of 5 when divided by 9, 6 or 8.
  20. 20.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?
  21. 21.Three temple bells ring every 9, 18 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Diya takes 50 seconds and Meera takes 80 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?
  23. 23.Kavya takes 45 seconds and Sneha 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?
  24. 24.Two tanks hold 80 litres and 140 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  25. 25.Find the smallest number bigger than 15 that leaves a remainder of 5 when divided by 15, 12 or 8.
  26. 26.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 6, 15 or 9.
  27. 27.Three temple bells ring every 6, 4 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.Three temple bells ring every 8, 5 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 6, 10 or 12.
  30. 30.Three temple bells ring every 10, 5 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.Two tanks hold 200 litres and 350 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  32. 32.Three temple bells ring every 10, 20 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.Three temple bells ring every 4, 30 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 15, 10 or 5.
  35. 35.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?
  36. 36.Dev takes 50 seconds and Sneha 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?
  37. 37.Three temple bells ring every 24, 6 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.Three temple bells ring every 20, 12 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.Three temple bells ring every 6, 4 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  40. 40.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 9, 15 or 12.

Answer key

  1. 45
  2. 34
  3. 28
  4. 180
  5. 12
  6. 91
  7. 39
  8. 28
  9. 21
  10. 72
  11. 450
  12. 72
  13. 60
  14. 122
  15. 40
  16. 225
  17. 90
  18. 14
  19. 77
  20. 12
  21. 36
  22. 400
  23. 180
  24. 20
  25. 125
  26. 92
  27. 60
  28. 120
  29. 63
  30. 120
  31. 50
  32. 60
  33. 60
  34. 34
  35. 40
  36. 300
  37. 120
  38. 60
  39. 24
  40. 182

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