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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 498 · 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.Two tanks hold 15 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  2. 2.Two tanks hold 250 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  3. 3.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 3 or 8.
  4. 4.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?
  5. 5.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?
  6. 6.A hall floor is 150 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  7. 7.Sneha takes 80 seconds and Tara 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?
  8. 8.Three temple bells ring every 30, 12 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.A hall floor is 160 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  10. 10.Find the smallest number bigger than 6 that leaves a remainder of 2 when divided by 6, 4 or 3.
  11. 11.Three temple bells ring every 15, 4 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.Three temple bells ring every 4, 15 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.Three temple bells ring every 30, 20 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.Kabir takes 50 seconds and Sneha 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?
  15. 15.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?
  16. 16.Tara takes 72 seconds and Ananya 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?
  17. 17.Two tanks hold 175 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  18. 18.Find the smallest number bigger than 15 that leaves a remainder of 7 when divided by 10, 8 or 15.
  19. 19.Three temple bells ring every 12, 4 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.Karan takes 90 seconds and Isha 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?
  21. 21.Farhan takes 72 seconds and Dev 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?
  22. 22.Three temple bells ring every 5, 8 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.Find the smallest number bigger than 6 that leaves a remainder of 2 when divided by 3, 6 or 5.
  24. 24.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 4, 6 or 15.
  25. 25.Manav takes 36 seconds and Aarav 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?
  26. 26.Find the smallest number bigger than 9 that leaves a remainder of 3 when divided by 6, 9 or 8.
  27. 27.Two tanks hold 135 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  28. 28.Three temple bells ring every 20, 24 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 3, 8 or 4.
  30. 30.Sneha takes 72 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?
  31. 31.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?
  32. 32.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 9, 4 or 10.
  33. 33.A hall floor is 420 cm long and 240 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  34. 34.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?
  35. 35.A hall floor is 200 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  36. 36.A hall floor is 210 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  37. 37.Isha takes 40 seconds and Saanvi 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?
  38. 38.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?
  39. 39.A hall floor is 200 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  40. 40.A hall floor is 360 cm long and 300 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?

Answer key

  1. 5
  2. 50
  3. 25
  4. 60
  5. 6
  6. 10
  7. 720
  8. 120
  9. 24
  10. 14
  11. 60
  12. 120
  13. 120
  14. 300
  15. 56
  16. 360
  17. 25
  18. 127
  19. 36
  20. 720
  21. 216
  22. 120
  23. 32
  24. 62
  25. 144
  26. 75
  27. 45
  28. 120
  29. 25
  30. 360
  31. 14
  32. 183
  33. 28
  34. 15
  35. 10
  36. 35
  37. 240
  38. 42
  39. 24
  40. 30

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