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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 207 · 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.Dev takes 50 seconds and Ishaan 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?
  2. 2.Farhan takes 80 seconds and Vivaan 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?
  3. 3.Two tanks hold 315 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  4. 4.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 8, 15 or 3.
  5. 5.Kabir takes 45 seconds and Priya 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?
  6. 6.Three temple bells ring every 10, 9 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.Kavya takes 50 seconds and Farhan 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.Two tanks hold 300 litres and 350 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  9. 9.A hall floor is 280 cm long and 240 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  10. 10.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 10 or 6.
  11. 11.A hall floor is 420 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  12. 12.Priya takes 36 seconds and Meera 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?
  13. 13.Kavya takes 40 seconds and Pooja 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?
  14. 14.Three temple bells ring every 4, 12 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  15. 15.Zoya takes 30 seconds and Sneha 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?
  16. 16.Three temple bells ring every 9, 5 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 3, 8 or 5.
  18. 18.Two tanks hold 20 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  19. 19.Three temple bells ring every 18, 5 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.A hall floor is 150 cm long and 125 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  21. 21.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?
  22. 22.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?
  23. 23.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?
  24. 24.A hall floor is 100 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  25. 25.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 3 or 10.
  26. 26.A hall floor is 315 cm long and 135 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  27. 27.Three temple bells ring every 30, 8 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.Two tanks hold 200 litres and 160 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  29. 29.A hall floor is 200 cm long and 125 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  30. 30.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 5, 4 or 12.
  31. 31.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 15, 10 or 5.
  32. 32.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?
  33. 33.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 6, 10 or 15.
  34. 34.Three temple bells ring every 6, 10 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.Rohan takes 48 seconds and Dev 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?
  36. 36.Diya takes 40 seconds and Meera 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?
  37. 37.Two tanks hold 175 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  38. 38.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 8, 3 or 9.
  39. 39.Two tanks hold 25 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  40. 40.Karan takes 72 seconds and Diya 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?

Answer key

  1. 150
  2. 240
  3. 45
  4. 122
  5. 225
  6. 90
  7. 200
  8. 50
  9. 42
  10. 32
  11. 14
  12. 108
  13. 120
  14. 36
  15. 360
  16. 45
  17. 121
  18. 10
  19. 90
  20. 30
  21. 120
  22. 5
  23. 20
  24. 10
  25. 32
  26. 21
  27. 120
  28. 40
  29. 40
  30. 63
  31. 34
  32. 12
  33. 32
  34. 120
  35. 144
  36. 360
  37. 25
  38. 73
  39. 5
  40. 360

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