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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 386 · 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 300 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  2. 2.Sneha 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?
  3. 3.Three temple bells ring every 10, 24 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.Find the smallest number bigger than 9 that leaves a remainder of 3 when divided by 9, 8 or 6.
  5. 5.Three temple bells ring every 12, 18 and 24 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 15 that leaves a remainder of 3 when divided by 5, 15 or 4.
  7. 7.Two tanks hold 45 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  8. 8.Three temple bells ring every 20, 24 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.Three temple bells ring every 5, 15 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 4, 5 or 6.
  11. 11.Three temple bells ring every 5, 6 and 4 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 6 that leaves a remainder of 1 when divided by 4, 3 or 6.
  13. 13.Isha takes 60 seconds and Karan 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?
  14. 14.A hall floor is 210 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  15. 15.Three temple bells ring every 30, 6 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.Two tanks hold 50 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  17. 17.Three temple bells ring every 4, 20 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 12 that leaves a remainder of 5 when divided by 10, 12 or 6.
  19. 19.Two tanks hold 90 litres and 135 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  20. 20.Three temple bells ring every 24, 10 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.Three temple bells ring every 18, 10 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Three temple bells ring every 10, 18 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.Pooja takes 45 seconds and Kabir 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.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 3 or 10.
  25. 25.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 10, 8 or 4.
  26. 26.Manav takes 90 seconds and Tara 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?
  27. 27.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?
  28. 28.Three temple bells ring every 18, 8 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Three temple bells ring every 8, 30 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.A hall floor is 125 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  31. 31.A hall floor is 270 cm long and 225 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  32. 32.A hall floor is 350 cm long and 250 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  33. 33.Diya takes 54 seconds and Manav 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?
  34. 34.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 8, 3 or 9.
  35. 35.Ishaan takes 54 seconds and Meera 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?
  36. 36.Two tanks hold 320 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.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 4 or 8.
  38. 38.A hall floor is 160 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  39. 39.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?
  40. 40.A hall floor is 160 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?

Answer key

  1. 15
  2. 120
  3. 120
  4. 75
  5. 72
  6. 63
  7. 15
  8. 120
  9. 120
  10. 61
  11. 60
  12. 13
  13. 180
  14. 21
  15. 120
  16. 10
  17. 60
  18. 65
  19. 45
  20. 120
  21. 90
  22. 90
  23. 90
  24. 31
  25. 43
  26. 360
  27. 45
  28. 72
  29. 120
  30. 15
  31. 30
  32. 35
  33. 270
  34. 73
  35. 432
  36. 40
  37. 26
  38. 40
  39. 14
  40. 24

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