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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 523 · 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.Zoya takes 36 seconds and Sneha 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?
  2. 2.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?
  3. 3.Two tanks hold 50 litres and 20 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 9, 6 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.A hall floor is 480 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  6. 6.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?
  7. 7.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 5, 15 or 6.
  8. 8.Vivaan takes 48 seconds and Priya 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?
  9. 9.Manav takes 48 seconds and Nisha 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?
  10. 10.Rohan takes 36 seconds and Aarav 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?
  11. 11.A hall floor is 300 cm long and 250 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  12. 12.A hall floor is 210 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  13. 13.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 5, 9 or 6.
  14. 14.Two tanks hold 105 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  15. 15.Three temple bells ring every 15, 8 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.Ishaan takes 72 seconds and Sneha 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?
  17. 17.Two tanks hold 40 litres and 70 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  18. 18.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?
  19. 19.Three temple bells ring every 12, 10 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 9, 15 or 3.
  21. 21.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 4, 6 or 3.
  22. 22.Karan takes 45 seconds and Dev 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?
  23. 23.Two tanks hold 50 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  24. 24.Three temple bells ring every 5, 24 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 6, 10 or 4.
  26. 26.Two tanks hold 60 litres and 160 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  27. 27.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 9, 8 or 3.
  28. 28.Three temple bells ring every 6, 24 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Three temple bells ring every 30, 20 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.Three temple bells ring every 9, 30 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.Two tanks hold 45 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  32. 32.Kabir takes 36 seconds and Ishaan 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 24, 20 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 5 or 6.
  35. 35.Aarav takes 60 seconds and Rahul 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?
  36. 36.Two tanks hold 150 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  37. 37.Three temple bells ring every 24, 4 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.Find the smallest number bigger than 12 that leaves a remainder of 5 when divided by 10, 6 or 12.
  39. 39.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?
  40. 40.Three temple bells ring every 5, 10 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 180
  2. 28
  3. 10
  4. 72
  5. 24
  6. 21
  7. 31
  8. 720
  9. 720
  10. 180
  11. 30
  12. 14
  13. 91
  14. 15
  15. 120
  16. 360
  17. 10
  18. 15
  19. 60
  20. 46
  21. 13
  22. 270
  23. 10
  24. 120
  25. 61
  26. 20
  27. 73
  28. 120
  29. 60
  30. 90
  31. 5
  32. 144
  33. 120
  34. 61
  35. 300
  36. 30
  37. 120
  38. 65
  39. 90
  40. 20

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