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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 59 · 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.Diya takes 72 seconds and Aditya 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?
  2. 2.A hall floor is 175 cm long and 50 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 12 that leaves a remainder of 3 when divided by 8, 4 or 12.
  4. 4.Find the smallest number bigger than 15 that leaves a remainder of 9 when divided by 10, 15 or 12.
  5. 5.Two tanks hold 200 litres and 240 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  6. 6.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?
  7. 7.A hall floor is 125 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  8. 8.Find the smallest number bigger than 8 that leaves a remainder of 4 when divided by 6, 5 or 8.
  9. 9.Two tanks hold 30 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  10. 10.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 6, 12 or 3.
  11. 11.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 9, 15 or 3.
  12. 12.Three temple bells ring every 5, 6 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.Two tanks hold 450 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.Sneha takes 80 seconds and Ishaan 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?
  15. 15.A hall floor is 350 cm long and 250 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 9, 4 or 12.
  17. 17.Meera takes 72 seconds and Rohan 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?
  18. 18.Diya 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.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 12, 15 or 4.
  20. 20.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?
  21. 21.Tara takes 48 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?
  22. 22.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?
  23. 23.Three temple bells ring every 12, 30 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Dev takes 72 seconds and Zoya 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.Three temple bells ring every 30, 4 and 15 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 10 that leaves a remainder of 1 when divided by 10, 4 or 6.
  27. 27.Two tanks hold 60 litres and 160 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  28. 28.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 8, 6 or 12.
  29. 29.Two tanks hold 225 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  30. 30.Three temple bells ring every 10, 18 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.Vivaan takes 54 seconds and Tara 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?
  32. 32.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 5, 3 or 12.
  33. 33.Three temple bells ring every 8, 24 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.Two tanks hold 135 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  35. 35.Two tanks hold 30 litres and 105 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 45 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?
  37. 37.Find the smallest number bigger than 10 that leaves a remainder of 4 when divided by 6, 10 or 9.
  38. 38.A hall floor is 315 cm long and 225 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  39. 39.Two tanks hold 225 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  40. 40.Kavya takes 72 seconds and Aarav 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. 216
  2. 14
  3. 27
  4. 69
  5. 40
  6. 21
  7. 15
  8. 124
  9. 10
  10. 14
  11. 47
  12. 60
  13. 50
  14. 720
  15. 35
  16. 38
  17. 360
  18. 400
  19. 61
  20. 35
  21. 240
  22. 20
  23. 60
  24. 360
  25. 60
  26. 61
  27. 20
  28. 27
  29. 45
  30. 90
  31. 270
  32. 61
  33. 72
  34. 45
  35. 15
  36. 360
  37. 94
  38. 35
  39. 25
  40. 360

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