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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 320 · 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, 5 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.A hall floor is 175 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  3. 3.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 4, 9 or 3.
  4. 4.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 4 or 8.
  5. 5.Zoya takes 90 seconds and Aarav 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?
  6. 6.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?
  7. 7.Nisha takes 80 seconds and Kavya 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?
  8. 8.Three temple bells ring every 8, 12 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.Ishaan takes 90 seconds and Dev 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?
  10. 10.Nisha takes 45 seconds and Tara 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?
  11. 11.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 4, 5 or 10.
  12. 12.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?
  13. 13.Three temple bells ring every 24, 20 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.Two tanks hold 175 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  15. 15.Diya takes 72 seconds and Ishaan 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?
  16. 16.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 9 or 4.
  17. 17.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?
  18. 18.Two tanks hold 45 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  19. 19.A hall floor is 320 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  20. 20.Two tanks hold 200 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  21. 21.A hall floor is 150 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  22. 22.Two tanks hold 60 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  23. 23.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 6, 12 or 3.
  24. 24.Vivaan takes 45 seconds and Ananya 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?
  25. 25.Vivaan takes 48 seconds and Aditya 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?
  26. 26.Two tanks hold 360 litres and 315 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  27. 27.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 5, 12 or 15.
  28. 28.Three temple bells ring every 6, 5 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Tara takes 90 seconds and Farhan 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?
  30. 30.Three temple bells ring every 15, 4 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.Two tanks hold 120 litres and 100 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 4, 6 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.A hall floor is 150 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  34. 34.A hall floor is 280 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  35. 35.Three temple bells ring every 12, 4 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.Zoya takes 45 seconds and Manav 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?
  37. 37.Two tanks hold 100 litres and 350 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  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.Three temple bells ring every 18, 9 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  40. 40.Three temple bells ring every 5, 10 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 60
  2. 21
  3. 37
  4. 121
  5. 180
  6. 10
  7. 720
  8. 120
  9. 450
  10. 720
  11. 22
  12. 12
  13. 120
  14. 25
  15. 720
  16. 181
  17. 40
  18. 15
  19. 24
  20. 25
  21. 20
  22. 30
  23. 14
  24. 90
  25. 720
  26. 45
  27. 62
  28. 120
  29. 720
  30. 60
  31. 20
  32. 60
  33. 15
  34. 21
  35. 60
  36. 360
  37. 50
  38. 25
  39. 72
  40. 60

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