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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 408 · 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 240 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  2. 2.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 6 or 3.
  3. 3.Arjun takes 75 seconds and Rahul 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.Three temple bells ring every 9, 4 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.A hall floor is 140 cm long and 120 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 6, 5 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.Three temple bells ring every 9, 8 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.A hall floor is 175 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  9. 9.Three temple bells ring every 5, 4 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.Two tanks hold 15 litres and 10 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  11. 11.A hall floor is 280 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  12. 12.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 8, 9 or 4.
  13. 13.Two tanks hold 450 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.Three temple bells ring every 4, 8 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  15. 15.Three temple bells ring every 9, 30 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.Tara takes 45 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?
  17. 17.Three temple bells ring every 10, 9 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.Find the smallest number bigger than 12 that leaves a remainder of 4 when divided by 12, 9 or 10.
  19. 19.A hall floor is 315 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  20. 20.Two tanks hold 40 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  21. 21.Three temple bells ring every 6, 15 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 15, 5 or 12.
  23. 23.Rohan takes 54 seconds and Tara 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?
  24. 24.Two tanks hold 25 litres and 35 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  25. 25.Three temple bells ring every 20, 30 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Saanvi takes 75 seconds and Aarav 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?
  27. 27.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?
  28. 28.Two tanks hold 150 litres and 175 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  29. 29.Zoya takes 30 seconds and Isha 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?
  30. 30.Sneha takes 30 seconds and Ananya 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?
  31. 31.Two tanks hold 50 litres and 70 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  32. 32.Pooja takes 60 seconds and Isha 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?
  33. 33.Three temple bells ring every 6, 8 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.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?
  35. 35.A hall floor is 250 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  36. 36.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 3, 12 or 5.
  37. 37.Two tanks hold 200 litres and 250 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  38. 38.Two tanks hold 140 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  39. 39.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 6 or 5.
  40. 40.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 5 or 3.

Answer key

  1. 24
  2. 13
  3. 150
  4. 36
  5. 42
  6. 120
  7. 72
  8. 42
  9. 60
  10. 5
  11. 14
  12. 73
  13. 50
  14. 72
  15. 90
  16. 360
  17. 90
  18. 184
  19. 14
  20. 5
  21. 30
  22. 64
  23. 270
  24. 5
  25. 120
  26. 150
  27. 50
  28. 25
  29. 150
  30. 150
  31. 10
  32. 240
  33. 72
  34. 35
  35. 20
  36. 62
  37. 50
  38. 20
  39. 61
  40. 62

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