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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 359 · 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 18, 24 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.Three temple bells ring every 4, 24 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.Three temple bells ring every 6, 15 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.Three temple bells ring every 10, 6 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.Kavya takes 60 seconds and Meera 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?
  6. 6.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 12 or 3.
  7. 7.Two tanks hold 30 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  8. 8.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?
  9. 9.Three temple bells ring every 6, 12 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.Three temple bells ring every 12, 18 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.Karan takes 90 seconds and Aditya 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?
  12. 12.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?
  13. 13.Three temple bells ring every 10, 12 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.Three temple bells ring every 6, 4 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  15. 15.Aarav takes 90 seconds and Diya 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 4, 20 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.Three temple bells ring every 6, 4 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.Find the smallest number bigger than 9 that leaves a remainder of 3 when divided by 5, 9 or 4.
  19. 19.A hall floor is 420 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  20. 20.A hall floor is 400 cm long and 350 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  21. 21.Find the smallest number bigger than 5 that leaves a remainder of 1 when divided by 3, 4 or 5.
  22. 22.Ananya takes 90 seconds and Isha 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?
  23. 23.Three temple bells ring every 4, 12 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 3, 9 or 15.
  25. 25.Three temple bells ring every 4, 5 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 12 that leaves a remainder of 1 when divided by 4, 12 or 8.
  27. 27.Manav takes 40 seconds and Sneha 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?
  28. 28.Two tanks hold 75 litres and 175 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 100 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  30. 30.Three temple bells ring every 6, 24 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.Three temple bells ring every 8, 30 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.Two tanks hold 15 litres and 35 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  33. 33.A hall floor is 240 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  34. 34.Two tanks hold 60 litres and 45 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 150 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  36. 36.Three temple bells ring every 24, 10 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  37. 37.Three temple bells ring every 15, 12 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.A hall floor is 225 cm long and 135 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  39. 39.Zoya takes 36 seconds and Kavya 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?
  40. 40.Nisha takes 90 seconds and Farhan 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?

Answer key

  1. 72
  2. 120
  3. 60
  4. 60
  5. 300
  6. 62
  7. 15
  8. 21
  9. 36
  10. 72
  11. 360
  12. 15
  13. 60
  14. 24
  15. 360
  16. 60
  17. 60
  18. 183
  19. 21
  20. 56
  21. 61
  22. 180
  23. 60
  24. 47
  25. 60
  26. 25
  27. 360
  28. 25
  29. 10
  30. 120
  31. 120
  32. 5
  33. 12
  34. 15
  35. 30
  36. 120
  37. 60
  38. 15
  39. 180
  40. 270

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