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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 431 · 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 250 litres and 450 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  2. 2.A hall floor is 210 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  3. 3.Two tanks hold 125 litres and 175 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  4. 4.Two tanks hold 300 litres and 250 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  5. 5.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 10, 5 or 4.
  6. 6.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?
  7. 7.Diya takes 40 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?
  8. 8.Three temple bells ring every 24, 5 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.A hall floor is 300 cm long and 120 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 9 that leaves a remainder of 3 when divided by 6, 9 or 5.
  11. 11.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?
  12. 12.Tara 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?
  13. 13.Two tanks hold 35 litres and 10 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.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?
  15. 15.A hall floor is 400 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  16. 16.A hall floor is 300 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  17. 17.Three temple bells ring every 24, 4 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.A hall floor is 250 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  19. 19.Meera takes 90 seconds and Priya 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?
  20. 20.A hall floor is 315 cm long and 225 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  21. 21.Three temple bells ring every 6, 5 and 18 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 1 when divided by 6, 8 or 10.
  23. 23.Two tanks hold 280 litres and 320 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  24. 24.Two tanks hold 105 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  25. 25.Rahul takes 54 seconds and Zoya 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?
  26. 26.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 6, 4 or 3.
  27. 27.A hall floor is 100 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  28. 28.Karan takes 40 seconds and Aarav 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?
  29. 29.A hall floor is 280 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  30. 30.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 15, 5 or 6.
  31. 31.Three temple bells ring every 5, 4 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.Two tanks hold 75 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  33. 33.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 5, 8 or 3.
  34. 34.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 3, 10 or 5.
  35. 35.Two tanks hold 450 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  36. 36.Two tanks hold 360 litres and 315 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  37. 37.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?
  38. 38.Two tanks hold 40 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  39. 39.Meera takes 80 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.A hall floor is 315 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?

Answer key

  1. 50
  2. 28
  3. 25
  4. 50
  5. 21
  6. 14
  7. 120
  8. 120
  9. 10
  10. 93
  11. 30
  12. 240
  13. 5
  14. 15
  15. 24
  16. 15
  17. 72
  18. 15
  19. 270
  20. 35
  21. 90
  22. 121
  23. 40
  24. 15
  25. 270
  26. 13
  27. 15
  28. 120
  29. 35
  30. 33
  31. 60
  32. 15
  33. 121
  34. 32
  35. 50
  36. 45
  37. 10
  38. 10
  39. 720
  40. 14

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