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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 405 · 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 100 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  2. 2.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?
  3. 3.Two tanks hold 175 litres and 125 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  4. 4.A hall floor is 400 cm long and 250 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  5. 5.Diya takes 80 seconds and Ishaan 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?
  6. 6.Two tanks hold 270 litres and 210 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  7. 7.Three temple bells ring every 6, 10 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.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?
  9. 9.A hall floor is 210 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  10. 10.Three temple bells ring every 12, 20 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.Find the smallest number bigger than 8 that leaves a remainder of 3 when divided by 5, 4 or 8.
  12. 12.A hall floor is 175 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  13. 13.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?
  14. 14.Aditya takes 40 seconds and Saanvi 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.Nisha takes 54 seconds and Aditya 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?
  16. 16.Three temple bells ring every 4, 5 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 3, 6 or 9.
  18. 18.Two tanks hold 40 litres and 140 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  19. 19.Saanvi takes 36 seconds and Rohan 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?
  20. 20.Isha takes 90 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?
  21. 21.Farhan takes 75 seconds and Nisha 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?
  22. 22.Two tanks hold 280 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  23. 23.A hall floor is 100 cm long and 75 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 4, 15 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.Two tanks hold 160 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  26. 26.Three temple bells ring every 20, 5 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.Three temple bells ring every 30, 4 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.Ishaan takes 75 seconds and Saanvi 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?
  29. 29.Find the smallest number bigger than 9 that leaves a remainder of 3 when divided by 4, 9 or 8.
  30. 30.Three temple bells ring every 10, 6 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.Two tanks hold 40 litres and 35 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  32. 32.Kavya takes 50 seconds and Manav 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?
  33. 33.Three temple bells ring every 18, 8 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.Three temple bells ring every 10, 8 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 4, 8 or 3.
  36. 36.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?
  37. 37.Farhan takes 45 seconds and Meera 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?
  38. 38.Three temple bells ring every 8, 12 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 15, 8 or 4.
  40. 40.Three temple bells ring every 10, 6 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 20
  2. 20
  3. 25
  4. 40
  5. 720
  6. 30
  7. 90
  8. 40
  9. 42
  10. 120
  11. 43
  12. 42
  13. 21
  14. 360
  15. 270
  16. 60
  17. 19
  18. 20
  19. 180
  20. 360
  21. 600
  22. 40
  23. 12
  24. 60
  25. 40
  26. 60
  27. 120
  28. 600
  29. 75
  30. 90
  31. 5
  32. 400
  33. 72
  34. 120
  35. 26
  36. 30
  37. 360
  38. 120
  39. 123
  40. 60

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