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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 157 · 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 24, 30 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.Saanvi takes 72 seconds and Sneha 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?
  3. 3.Three temple bells ring every 20, 10 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.Three temple bells ring every 12, 15 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.Meera takes 30 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?
  6. 6.Three temple bells ring every 10, 15 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 8 or 3.
  8. 8.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 5, 12 or 6.
  9. 9.Three temple bells ring every 8, 10 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.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?
  11. 11.Rahul takes 45 seconds and Pooja 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?
  12. 12.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?
  13. 13.Arjun takes 50 seconds and Isha 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?
  14. 14.Two tanks hold 360 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  15. 15.Two tanks hold 100 litres and 250 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  16. 16.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?
  17. 17.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 3, 9 or 4.
  18. 18.A hall floor is 360 cm long and 225 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  19. 19.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?
  20. 20.A hall floor is 480 cm long and 300 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 9, 4 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.A hall floor is 250 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  23. 23.Ananya takes 90 seconds and Vivaan takes 50 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?
  24. 24.Find the smallest number bigger than 5 that leaves a remainder of 1 when divided by 3, 4 or 5.
  25. 25.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 10, 5 or 4.
  26. 26.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 4, 8 or 12.
  27. 27.Vivaan takes 30 seconds and Rahul 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?
  28. 28.Two tanks hold 10 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  29. 29.Arjun takes 36 seconds and Pooja 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.Two tanks hold 75 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  31. 31.Tara takes 45 seconds and Vivaan 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?
  32. 32.Three temple bells ring every 6, 8 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.Two tanks hold 75 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  34. 34.Tara takes 40 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?
  35. 35.Three temple bells ring every 10, 8 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.Two tanks hold 210 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  37. 37.Three temple bells ring every 5, 30 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.Farhan takes 40 seconds and Arjun 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?
  39. 39.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 4, 9 or 12.
  40. 40.Three temple bells ring every 18, 9 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 120
  2. 360
  3. 40
  4. 60
  5. 270
  6. 120
  7. 25
  8. 63
  9. 120
  10. 14
  11. 225
  12. 36
  13. 450
  14. 40
  15. 50
  16. 30
  17. 37
  18. 40
  19. 56
  20. 40
  21. 36
  22. 15
  23. 450
  24. 61
  25. 23
  26. 25
  27. 360
  28. 5
  29. 144
  30. 25
  31. 225
  32. 120
  33. 15
  34. 120
  35. 40
  36. 30
  37. 120
  38. 360
  39. 37
  40. 72

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