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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 60 · 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.A hall floor is 125 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  2. 2.Aarav takes 30 seconds and Sneha 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?
  3. 3.Three temple bells ring every 10, 12 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.A hall floor is 350 cm long and 300 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  5. 5.Sneha takes 36 seconds and Kabir 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?
  6. 6.Three temple bells ring every 5, 18 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.Three temple bells ring every 5, 8 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 9, 4 or 10.
  9. 9.Three temple bells ring every 15, 6 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.Three temple bells ring every 5, 8 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.Three temple bells ring every 18, 24 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.Three temple bells ring every 6, 18 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.Three temple bells ring every 9, 12 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.Two tanks hold 50 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.Diya takes 90 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?
  16. 16.A hall floor is 240 cm long and 90 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 6 that leaves a remainder of 1 when divided by 4, 6 or 5.
  18. 18.Two tanks hold 120 litres and 280 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  19. 19.Vivaan takes 54 seconds and Karan 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?
  20. 20.Ananya takes 50 seconds and Aditya 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?
  21. 21.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 5, 12 or 8.
  22. 22.Nisha takes 60 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?
  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.Three temple bells ring every 30, 10 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.A hall floor is 480 cm long and 420 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  26. 26.Three temple bells ring every 8, 6 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.Two tanks hold 70 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  28. 28.A hall floor is 75 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  29. 29.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?
  30. 30.Two tanks hold 140 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  31. 31.Three temple bells ring every 10, 5 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.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?
  33. 33.A hall floor is 120 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  34. 34.Two tanks hold 225 litres and 125 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  35. 35.Three temple bells ring every 24, 15 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 15, 6 or 4.
  37. 37.Meera takes 45 seconds and Rahul 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?
  38. 38.Aditya takes 45 seconds and Diya 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?
  39. 39.Two tanks hold 20 litres and 70 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  40. 40.Three temple bells ring every 6, 20 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 10
  2. 240
  3. 60
  4. 42
  5. 180
  6. 90
  7. 120
  8. 181
  9. 60
  10. 40
  11. 72
  12. 90
  13. 36
  14. 10
  15. 180
  16. 24
  17. 61
  18. 40
  19. 216
  20. 150
  21. 123
  22. 540
  23. 20
  24. 60
  25. 56
  26. 120
  27. 10
  28. 6
  29. 36
  30. 20
  31. 90
  32. 15
  33. 6
  34. 25
  35. 120
  36. 63
  37. 180
  38. 90
  39. 10
  40. 120

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