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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 469 · 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.Sneha takes 30 seconds and Farhan 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?
  2. 2.A hall floor is 315 cm long and 270 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  3. 3.Kabir takes 80 seconds and Nisha 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?
  4. 4.Aarav 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?
  5. 5.Three temple bells ring every 30, 8 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 3, 6 or 10.
  7. 7.Two tanks hold 75 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  8. 8.Three temple bells ring every 6, 24 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.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?
  10. 10.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?
  11. 11.Two tanks hold 30 litres and 25 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  12. 12.Two tanks hold 70 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  13. 13.Three temple bells ring every 4, 24 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.Ananya 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?
  15. 15.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 8, 4 or 9.
  16. 16.Tara 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?
  17. 17.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?
  18. 18.Saanvi takes 48 seconds and Meera 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?
  19. 19.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 12, 4 or 9.
  20. 20.Kavya takes 30 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?
  21. 21.Diya takes 30 seconds and Rohan 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?
  22. 22.Three temple bells ring every 12, 18 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.Two tanks hold 60 litres and 105 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  24. 24.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 5, 12 or 3.
  25. 25.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?
  26. 26.Find the smallest number bigger than 6 that leaves a remainder of 2 when divided by 3, 6 or 5.
  27. 27.Three temple bells ring every 12, 20 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.Ananya takes 72 seconds and Karan 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?
  29. 29.Three temple bells ring every 8, 24 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.Three temple bells ring every 18, 15 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.Three temple bells ring every 30, 12 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.Farhan takes 75 seconds and Kabir 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?
  33. 33.Three temple bells ring every 18, 12 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.A hall floor is 80 cm long and 60 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 5, 9 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.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?
  37. 37.A hall floor is 140 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  38. 38.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 3, 10 or 12.
  39. 39.Two tanks hold 360 litres and 160 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  40. 40.Kabir takes 90 seconds and Aditya 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. 90
  2. 42
  3. 720
  4. 360
  5. 120
  6. 32
  7. 15
  8. 120
  9. 21
  10. 14
  11. 5
  12. 10
  13. 120
  14. 108
  15. 73
  16. 270
  17. 14
  18. 720
  19. 39
  20. 90
  21. 360
  22. 36
  23. 15
  24. 61
  25. 14
  26. 32
  27. 60
  28. 360
  29. 72
  30. 90
  31. 60
  32. 225
  33. 36
  34. 12
  35. 90
  36. 56
  37. 28
  38. 61
  39. 40
  40. 360

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