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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 365 · 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.Farhan takes 40 seconds and Dev 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?
  2. 2.Two tanks hold 50 litres and 125 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  3. 3.A hall floor is 160 cm long and 140 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  4. 4.Three temple bells ring every 15, 6 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 8, 10 or 15.
  6. 6.Three temple bells ring every 5, 6 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.Find the smallest number bigger than 12 that leaves a remainder of 6 when divided by 8, 12 or 9.
  8. 8.Aarav takes 75 seconds and Pooja 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?
  9. 9.A hall floor is 200 cm long and 175 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  10. 10.Priya takes 50 seconds and Pooja 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?
  11. 11.Three temple bells ring every 15, 10 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.A hall floor is 320 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  13. 13.Three temple bells ring every 10, 12 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.Two tanks hold 20 litres and 25 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  15. 15.Ananya takes 60 seconds and Saanvi takes 50 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?
  16. 16.Three temple bells ring every 4, 30 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.Arjun takes 36 seconds and Nisha 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?
  18. 18.Two tanks hold 40 litres and 50 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 20, 4 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.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?
  21. 21.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 3, 8 or 15.
  22. 22.Three temple bells ring every 4, 20 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.Three temple bells ring every 8, 6 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Three temple bells ring every 4, 6 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.Dev takes 36 seconds and Ananya 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?
  26. 26.Find the smallest number bigger than 10 that leaves a remainder of 5 when divided by 10, 6 or 9.
  27. 27.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 3, 15 or 4.
  28. 28.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?
  29. 29.Two tanks hold 150 litres and 210 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  30. 30.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?
  31. 31.Three temple bells ring every 20, 5 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.Dev takes 80 seconds and Zoya takes 72 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 15, 10 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.Three temple bells ring every 30, 6 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.Three temple bells ring every 18, 9 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.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?
  37. 37.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?
  38. 38.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 9, 3 or 6.
  39. 39.Three temple bells ring every 15, 18 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  40. 40.A hall floor is 300 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?

Answer key

  1. 360
  2. 25
  3. 56
  4. 60
  5. 122
  6. 60
  7. 78
  8. 600
  9. 56
  10. 150
  11. 60
  12. 40
  13. 60
  14. 5
  15. 300
  16. 120
  17. 180
  18. 10
  19. 60
  20. 90
  21. 122
  22. 60
  23. 24
  24. 24
  25. 108
  26. 95
  27. 62
  28. 15
  29. 30
  30. 120
  31. 60
  32. 720
  33. 30
  34. 120
  35. 90
  36. 35
  37. 28
  38. 20
  39. 90
  40. 10

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