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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 134 · 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 20 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  2. 2.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 3, 10 or 5.
  3. 3.Two tanks hold 100 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  4. 4.Isha takes 45 seconds and Aarav 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?
  5. 5.Isha takes 36 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?
  6. 6.A hall floor is 175 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  7. 7.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?
  8. 8.Two tanks hold 150 litres and 125 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  9. 9.Rohan takes 54 seconds and Kavya 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?
  10. 10.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 8, 4 or 5.
  11. 11.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 12, 4 or 15.
  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.A hall floor is 240 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  14. 14.Dev takes 60 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?
  15. 15.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?
  16. 16.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 9, 4 or 3.
  17. 17.A hall floor is 180 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  18. 18.Two tanks hold 35 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  19. 19.Three temple bells ring every 5, 8 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.Kabir takes 30 seconds and Isha 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?
  21. 21.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?
  22. 22.Find the smallest number bigger than 10 that leaves a remainder of 4 when divided by 10, 8 or 5.
  23. 23.Manav takes 50 seconds and Zoya 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?
  24. 24.Three temple bells ring every 8, 9 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 280 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  26. 26.Karan takes 60 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?
  27. 27.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 5, 9 or 4.
  28. 28.Two tanks hold 100 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  29. 29.Aditya takes 54 seconds and Manav 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?
  30. 30.Three temple bells ring every 20, 24 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.Meera takes 90 seconds and Rahul 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?
  32. 32.Three temple bells ring every 12, 18 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.A hall floor is 240 cm long and 210 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  34. 34.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?
  35. 35.Two tanks hold 90 litres and 20 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 8, 18 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  37. 37.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?
  38. 38.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?
  39. 39.A hall floor is 125 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  40. 40.Three temple bells ring every 9, 8 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 10
  2. 32
  3. 20
  4. 180
  5. 180
  6. 21
  7. 6
  8. 25
  9. 108
  10. 42
  11. 63
  12. 15
  13. 30
  14. 360
  15. 120
  16. 38
  17. 6
  18. 5
  19. 120
  20. 270
  21. 60
  22. 44
  23. 200
  24. 72
  25. 14
  26. 540
  27. 181
  28. 25
  29. 270
  30. 120
  31. 270
  32. 36
  33. 56
  34. 120
  35. 10
  36. 72
  37. 35
  38. 40
  39. 20
  40. 72

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