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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 507 · 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 280 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  2. 2.Farhan takes 45 seconds and Diya 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?
  3. 3.Three temple bells ring every 6, 8 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.A hall floor is 125 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  5. 5.Three temple bells ring every 10, 5 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.Two tanks hold 105 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  7. 7.Vivaan takes 90 seconds and Dev 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?
  8. 8.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 6, 3 or 10.
  9. 9.Three temple bells ring every 10, 8 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.Two tanks hold 320 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  11. 11.Three temple bells ring every 18, 12 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.Three temple bells ring every 12, 30 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.Find the smallest number bigger than 5 that leaves a remainder of 2 when divided by 4, 3 or 5.
  14. 14.Three temple bells ring every 24, 15 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  15. 15.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?
  16. 16.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?
  17. 17.Two tanks hold 100 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  18. 18.Manav takes 48 seconds and Kavya 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?
  19. 19.Two tanks hold 60 litres and 210 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  20. 20.A hall floor is 210 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  21. 21.Two tanks hold 240 litres and 210 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  22. 22.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 3, 4 or 12.
  23. 23.Aarav takes 30 seconds and Isha 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?
  24. 24.Karan takes 72 seconds and Nisha 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?
  25. 25.Two tanks hold 15 litres and 10 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  26. 26.Three temple bells ring every 9, 5 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.Find the smallest number bigger than 15 that leaves a remainder of 7 when divided by 10, 9 or 15.
  28. 28.Three temple bells ring every 20, 6 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Manav takes 48 seconds and Pooja 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?
  30. 30.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 3, 8 or 4.
  31. 31.Aditya takes 48 seconds and Farhan 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?
  32. 32.Three temple bells ring every 10, 5 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.Three temple bells ring every 18, 9 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.Three temple bells ring every 24, 20 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.Aditya takes 45 seconds and Rahul 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?
  36. 36.Two tanks hold 125 litres and 100 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 1 when divided by 4, 5 or 12.
  38. 38.Two tanks hold 75 litres and 125 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  39. 39.Two tanks hold 150 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  40. 40.Two tanks hold 90 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?

Answer key

  1. 35
  2. 720
  3. 72
  4. 20
  5. 40
  6. 15
  7. 360
  8. 32
  9. 120
  10. 40
  11. 36
  12. 60
  13. 62
  14. 120
  15. 45
  16. 30
  17. 20
  18. 240
  19. 30
  20. 35
  21. 30
  22. 14
  23. 150
  24. 360
  25. 5
  26. 90
  27. 97
  28. 120
  29. 144
  30. 25
  31. 432
  32. 30
  33. 90
  34. 120
  35. 180
  36. 25
  37. 61
  38. 25
  39. 30
  40. 15

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