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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 449 · 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.Two tanks hold 35 litres and 15 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  2. 2.A hall floor is 200 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  3. 3.A hall floor is 225 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  4. 4.A hall floor is 360 cm long and 135 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  5. 5.Arjun takes 90 seconds and Ishaan 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?
  6. 6.Two tanks hold 175 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  7. 7.Two tanks hold 225 litres and 270 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  8. 8.A hall floor is 100 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  9. 9.Two tanks hold 160 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  10. 10.Three temple bells ring every 15, 24 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.A hall floor is 400 cm long and 250 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  12. 12.Diya 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?
  13. 13.Two tanks hold 405 litres and 315 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.Dev takes 36 seconds and Aditya 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?
  15. 15.Three temple bells ring every 9, 4 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 8, 3 or 4.
  17. 17.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 8, 15 or 5.
  18. 18.Ananya takes 30 seconds and Rohan 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?
  19. 19.Aarav takes 36 seconds and Diya 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?
  20. 20.Aditya takes 36 seconds and Ananya 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?
  21. 21.Kavya takes 36 seconds and Ishaan 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?
  22. 22.Two tanks hold 75 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  23. 23.Two tanks hold 80 litres and 70 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 6, 8 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.Three temple bells ring every 24, 8 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 8 or 5.
  27. 27.A hall floor is 400 cm long and 350 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  28. 28.Three temple bells ring every 8, 15 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.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?
  30. 30.Aditya takes 45 seconds and Zoya 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?
  31. 31.Manav takes 60 seconds and Kabir 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?
  32. 32.Two tanks hold 80 litres and 360 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  33. 33.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 4, 6 or 15.
  34. 34.Three temple bells ring every 24, 8 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.Three temple bells ring every 15, 4 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.Two tanks hold 405 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.Find the smallest number bigger than 5 that leaves a remainder of 2 when divided by 5, 3 or 4.
  38. 38.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 8, 6 or 3.
  39. 39.Zoya takes 90 seconds and Aarav 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?
  40. 40.A hall floor is 140 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?

Answer key

  1. 5
  2. 24
  3. 10
  4. 24
  5. 270
  6. 25
  7. 45
  8. 12
  9. 20
  10. 120
  11. 40
  12. 180
  13. 45
  14. 180
  15. 36
  16. 25
  17. 124
  18. 120
  19. 108
  20. 720
  21. 108
  22. 25
  23. 10
  24. 24
  25. 120
  26. 121
  27. 56
  28. 120
  29. 56
  30. 360
  31. 180
  32. 40
  33. 63
  34. 120
  35. 60
  36. 45
  37. 62
  38. 26
  39. 270
  40. 14

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