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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 36 · 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.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 8, 3 or 12.
  2. 2.Two tanks hold 25 litres and 10 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  3. 3.Aditya takes 30 seconds and Tara 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?
  4. 4.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?
  5. 5.Three temple bells ring every 5, 6 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.A hall floor is 90 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  7. 7.Two tanks hold 200 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  8. 8.Aditya takes 30 seconds and Ananya 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?
  9. 9.Ishaan takes 54 seconds and Saanvi 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?
  10. 10.Two tanks hold 225 litres and 135 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  11. 11.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?
  12. 12.A hall floor is 140 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  13. 13.Manav takes 60 seconds and Tara 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?
  14. 14.Three temple bells ring every 15, 10 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  15. 15.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 5 or 3.
  16. 16.A hall floor is 100 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  17. 17.Saanvi 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?
  18. 18.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?
  19. 19.Three temple bells ring every 4, 30 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.Two tanks hold 50 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  21. 21.Zoya takes 50 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?
  22. 22.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 4 or 3.
  23. 23.Three temple bells ring every 6, 10 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 3 or 4.
  25. 25.A hall floor is 360 cm long and 315 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  26. 26.Two tanks hold 160 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  27. 27.Three temple bells ring every 12, 5 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.Diya takes 75 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?
  29. 29.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?
  30. 30.Two tanks hold 200 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  31. 31.Two tanks hold 45 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  32. 32.Three temple bells ring every 24, 5 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 3, 8 or 4.
  34. 34.Three temple bells ring every 8, 10 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.Two tanks hold 180 litres and 315 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  36. 36.Arjun takes 60 seconds and Ishaan 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?
  37. 37.Dev takes 60 seconds and Rohan 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?
  38. 38.Three temple bells ring every 8, 20 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.Two tanks hold 210 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  40. 40.A hall floor is 120 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?

Answer key

  1. 26
  2. 5
  3. 360
  4. 40
  5. 60
  6. 6
  7. 40
  8. 240
  9. 270
  10. 45
  11. 21
  12. 21
  13. 300
  14. 120
  15. 61
  16. 20
  17. 720
  18. 14
  19. 60
  20. 10
  21. 200
  22. 14
  23. 60
  24. 61
  25. 56
  26. 40
  27. 60
  28. 450
  29. 35
  30. 50
  31. 15
  32. 120
  33. 25
  34. 120
  35. 45
  36. 120
  37. 180
  38. 120
  39. 30
  40. 30

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