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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 199 · 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.Diya takes 36 seconds and Sneha 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?
  2. 2.Three temple bells ring every 4, 15 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.Three temple bells ring every 12, 20 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.A hall floor is 240 cm long and 210 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  5. 5.A hall floor is 225 cm long and 135 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 12 that leaves a remainder of 2 when divided by 6, 12 or 5.
  7. 7.Three temple bells ring every 5, 8 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.A hall floor is 120 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  9. 9.Find the smallest number bigger than 5 that leaves a remainder of 2 when divided by 4, 3 or 5.
  10. 10.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 5, 15 or 8.
  11. 11.Three temple bells ring every 8, 5 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.Arjun takes 45 seconds and Priya 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?
  13. 13.Two tanks hold 180 litres and 150 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 5, 18 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  15. 15.Two tanks hold 60 litres and 90 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 8, 20 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.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?
  18. 18.Three temple bells ring every 5, 8 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.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?
  20. 20.Two tanks hold 400 litres and 450 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  21. 21.Find the smallest number bigger than 15 that leaves a remainder of 8 when divided by 15, 12 or 9.
  22. 22.Two tanks hold 150 litres and 350 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  23. 23.A hall floor is 180 cm long and 135 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  24. 24.Rohan takes 60 seconds and Pooja 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?
  25. 25.Two tanks hold 360 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  26. 26.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?
  27. 27.Three temple bells ring every 9, 5 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.Three temple bells ring every 5, 12 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Three temple bells ring every 5, 4 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.Three temple bells ring every 10, 4 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.Ananya takes 40 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?
  32. 32.Two tanks hold 400 litres and 250 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  33. 33.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?
  34. 34.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 6, 8 or 9.
  35. 35.Two tanks hold 175 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  36. 36.Ishaan takes 90 seconds and Rohan 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?
  37. 37.Find the smallest number bigger than 8 that leaves a remainder of 3 when divided by 5, 4 or 8.
  38. 38.Karan takes 36 seconds and Manav 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?
  39. 39.A hall floor is 90 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  40. 40.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?

Answer key

  1. 180
  2. 60
  3. 120
  4. 56
  5. 15
  6. 62
  7. 120
  8. 30
  9. 62
  10. 123
  11. 40
  12. 225
  13. 30
  14. 90
  15. 30
  16. 40
  17. 60
  18. 120
  19. 10
  20. 50
  21. 188
  22. 50
  23. 12
  24. 180
  25. 40
  26. 35
  27. 90
  28. 120
  29. 40
  30. 40
  31. 240
  32. 50
  33. 5
  34. 73
  35. 25
  36. 720
  37. 43
  38. 180
  39. 6
  40. 50

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