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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 325 · 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.Three temple bells ring every 12, 18 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.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?
  3. 3.Three temple bells ring every 12, 8 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.A hall floor is 315 cm long and 180 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 6, 24 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.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?
  7. 7.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 4, 6 or 8.
  8. 8.Three temple bells ring every 20, 15 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.Two tanks hold 135 litres and 105 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  10. 10.Two tanks hold 280 litres and 160 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  11. 11.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 8, 6 or 4.
  12. 12.Three temple bells ring every 9, 24 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.Three temple bells ring every 18, 30 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 9, 10 or 3.
  15. 15.A hall floor is 350 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  16. 16.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 5, 6 or 12.
  17. 17.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 8, 10 or 4.
  18. 18.Aarav takes 50 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?
  19. 19.Diya takes 80 seconds and Karan 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?
  20. 20.Two tanks hold 225 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  21. 21.Three temple bells ring every 30, 6 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 8, 6 or 4.
  23. 23.Kabir takes 60 seconds and Ananya 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.Ananya takes 40 seconds and Dev 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?
  25. 25.A hall floor is 175 cm long and 125 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  26. 26.A hall floor is 175 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  27. 27.Find the smallest number bigger than 12 that leaves a remainder of 7 when divided by 12, 9 or 10.
  28. 28.Two tanks hold 120 litres and 270 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 50 litres and 80 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 135 litres and 360 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  31. 31.A hall floor is 160 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  32. 32.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 3, 5 or 9.
  33. 33.Three temple bells ring every 6, 4 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.Three temple bells ring every 10, 6 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.Arjun takes 90 seconds and Meera 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?
  36. 36.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?
  37. 37.Rohan takes 48 seconds and Priya 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?
  38. 38.Three temple bells ring every 4, 18 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.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?
  40. 40.Diya takes 60 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?

Answer key

  1. 36
  2. 25
  3. 120
  4. 28
  5. 72
  6. 35
  7. 25
  8. 60
  9. 15
  10. 40
  11. 25
  12. 72
  13. 90
  14. 92
  15. 21
  16. 62
  17. 42
  18. 400
  19. 720
  20. 25
  21. 120
  22. 26
  23. 180
  24. 120
  25. 35
  26. 28
  27. 187
  28. 30
  29. 10
  30. 45
  31. 24
  32. 46
  33. 36
  34. 120
  35. 720
  36. 21
  37. 144
  38. 36
  39. 24
  40. 180

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