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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 392 · 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).

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  1. 1.A hall floor is 420 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  2. 2.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?
  3. 3.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 8, 10 or 3.
  4. 4.Three temple bells ring every 12, 24 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.Aarav takes 30 seconds and Meera 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?
  6. 6.Saanvi takes 60 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?
  7. 7.Dev takes 45 seconds and Pooja 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?
  8. 8.Meera takes 80 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?
  9. 9.Three temple bells ring every 4, 10 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.Isha takes 60 seconds and Priya takes 90 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?
  11. 11.Two tanks hold 405 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  12. 12.Vivaan takes 36 seconds and Priya 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?
  13. 13.A hall floor is 250 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  14. 14.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?
  15. 15.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?
  16. 16.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 3 or 9.
  17. 17.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 10, 3 or 15.
  18. 18.A hall floor is 160 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  19. 19.Three temple bells ring every 18, 6 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 8, 15 or 3.
  21. 21.Three temple bells ring every 12, 15 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 3, 4 or 6.
  23. 23.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 9, 8 or 6.
  24. 24.Nisha takes 72 seconds and Sneha 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?
  25. 25.Three temple bells ring every 18, 30 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Manav takes 54 seconds and Priya 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?
  27. 27.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 10, 15 or 6.
  28. 28.Two tanks hold 50 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  29. 29.Two tanks hold 200 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  30. 30.Two tanks hold 60 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  31. 31.Dev takes 30 seconds and Sneha 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?
  32. 32.Sneha takes 48 seconds and Farhan 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?
  33. 33.Three temple bells ring every 10, 6 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.Find the smallest number bigger than 15 that leaves a remainder of 6 when divided by 15, 10 or 9.
  35. 35.Three temple bells ring every 20, 15 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.Vivaan takes 60 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?
  37. 37.Two tanks hold 180 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  38. 38.Three temple bells ring every 20, 15 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.Tara takes 54 seconds and Arjun 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?
  40. 40.A hall floor is 200 cm long and 125 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?

Answer key

  1. 14
  2. 40
  3. 121
  4. 120
  5. 240
  6. 300
  7. 90
  8. 720
  9. 40
  10. 180
  11. 45
  12. 180
  13. 20
  14. 35
  15. 40
  16. 38
  17. 31
  18. 40
  19. 72
  20. 121
  21. 60
  22. 13
  23. 74
  24. 216
  25. 90
  26. 270
  27. 33
  28. 10
  29. 25
  30. 10
  31. 90
  32. 240
  33. 90
  34. 96
  35. 60
  36. 540
  37. 20
  38. 120
  39. 108
  40. 40

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