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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 423 · 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 400 cm long and 250 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  2. 2.Aarav takes 60 seconds and Meera 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?
  3. 3.Two tanks hold 250 litres and 300 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  4. 4.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?
  5. 5.A hall floor is 400 cm long and 150 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 15 that leaves a remainder of 2 when divided by 5, 8 or 15.
  7. 7.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?
  8. 8.Three temple bells ring every 30, 9 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.Sneha takes 72 seconds and Karan takes 54 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.Two tanks hold 180 litres and 225 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 250 cm long and 100 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 2 when divided by 8, 9 or 3.
  13. 13.Two tanks hold 20 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 6, 9 or 12.
  15. 15.Two tanks hold 105 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  16. 16.Three temple bells ring every 15, 30 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.Three temple bells ring every 30, 24 and 4 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 10 that leaves a remainder of 2 when divided by 6, 10 or 4.
  19. 19.Three temple bells ring every 15, 30 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.Three temple bells ring every 20, 6 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.Two tanks hold 75 litres and 105 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  22. 22.Two tanks hold 225 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  23. 23.Aarav takes 40 seconds and Karan 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?
  24. 24.A hall floor is 200 cm long and 120 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, 4 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Three temple bells ring every 30, 8 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.Two tanks hold 100 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  28. 28.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 4, 8 or 12.
  29. 29.Two tanks hold 30 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  30. 30.Two tanks hold 225 litres and 270 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  31. 31.Find the smallest number bigger than 9 that leaves a remainder of 3 when divided by 9, 4 or 5.
  32. 32.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 3, 6 or 8.
  33. 33.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?
  34. 34.Isha takes 50 seconds and Rohan 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?
  35. 35.A hall floor is 250 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  36. 36.Three temple bells ring every 8, 24 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  37. 37.Two tanks hold 15 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  38. 38.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 8, 9 or 12.
  39. 39.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 12, 15 or 8.
  40. 40.Two tanks hold 120 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?

Answer key

  1. 40
  2. 120
  3. 50
  4. 60
  5. 24
  6. 122
  7. 40
  8. 90
  9. 216
  10. 45
  11. 10
  12. 74
  13. 10
  14. 37
  15. 15
  16. 120
  17. 120
  18. 62
  19. 60
  20. 60
  21. 15
  22. 45
  23. 360
  24. 15
  25. 72
  26. 120
  27. 25
  28. 25
  29. 10
  30. 45
  31. 183
  32. 26
  33. 60
  34. 450
  35. 15
  36. 120
  37. 5
  38. 74
  39. 122
  40. 15

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