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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 84 · 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).

NameDateTime takenScore ___ / 40
  1. 1.A hall floor is 150 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  2. 2.A hall floor is 210 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  3. 3.Priya takes 54 seconds and Tara 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?
  4. 4.Zoya takes 48 seconds and Aarav 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?
  5. 5.Three temple bells ring every 5, 30 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.A hall floor is 140 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  7. 7.A hall floor is 175 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  8. 8.A hall floor is 150 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  9. 9.Two tanks hold 210 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  10. 10.Zoya takes 40 seconds and Vivaan 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?
  11. 11.Three temple bells ring every 6, 18 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 10 or 8.
  13. 13.Three temple bells ring every 12, 15 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.Three temple bells ring every 9, 24 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  15. 15.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?
  16. 16.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 3, 4 or 12.
  17. 17.Three temple bells ring every 18, 12 and 6 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 15 that leaves a remainder of 3 when divided by 4, 15 or 9.
  19. 19.A hall floor is 480 cm long and 420 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  20. 20.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 10, 4 or 12.
  21. 21.Pooja takes 45 seconds and Meera 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?
  22. 22.Dev takes 36 seconds and Tara 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?
  23. 23.Tara takes 30 seconds and Farhan 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?
  24. 24.A hall floor is 135 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  25. 25.Three temple bells ring every 24, 30 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Two tanks hold 240 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  27. 27.A hall floor is 350 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  28. 28.Three temple bells ring every 8, 4 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Sneha takes 60 seconds and Ishaan 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.Three temple bells ring every 8, 10 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.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?
  32. 32.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 5, 3 or 9.
  33. 33.A hall floor is 360 cm long and 135 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  34. 34.Three temple bells ring every 8, 5 and 24 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 10 that leaves a remainder of 1 when divided by 10, 4 or 6.
  36. 36.Two tanks hold 175 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  37. 37.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?
  38. 38.Two tanks hold 120 litres and 75 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 10 that leaves a remainder of 2 when divided by 3, 10 or 5.
  40. 40.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 10, 8 or 6.

Answer key

  1. 20
  2. 42
  3. 432
  4. 144
  5. 120
  6. 35
  7. 14
  8. 6
  9. 30
  10. 120
  11. 90
  12. 122
  13. 60
  14. 72
  15. 28
  16. 13
  17. 36
  18. 183
  19. 56
  20. 62
  21. 90
  22. 144
  23. 240
  24. 6
  25. 120
  26. 30
  27. 28
  28. 40
  29. 300
  30. 40
  31. 72
  32. 47
  33. 24
  34. 120
  35. 61
  36. 25
  37. 6
  38. 15
  39. 32
  40. 123

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