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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 196 · 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 120 litres and 80 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 200 cm long and 125 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  3. 3.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?
  4. 4.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 6, 10 or 15.
  5. 5.Three temple bells ring every 4, 10 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.Two tanks hold 45 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  7. 7.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 5, 6 or 10.
  8. 8.Nisha takes 40 seconds and Diya 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?
  9. 9.Three temple bells ring every 24, 18 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.Two tanks hold 100 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  11. 11.Three temple bells ring every 10, 8 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 9, 10 or 15.
  13. 13.A hall floor is 150 cm long and 125 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  14. 14.Rohan takes 60 seconds and Kabir 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.Two tanks hold 40 litres and 25 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  16. 16.A hall floor is 480 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  17. 17.Two tanks hold 80 litres and 360 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  18. 18.A hall floor is 210 cm long and 60 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 15, 24 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.Three temple bells ring every 15, 6 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.Two tanks hold 360 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  22. 22.A hall floor is 420 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  23. 23.Karan 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?
  24. 24.Three temple bells ring every 24, 10 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.Kabir takes 90 seconds and Saanvi 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?
  26. 26.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 8, 6 or 15.
  27. 27.Two tanks hold 120 litres and 320 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, 8 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.A hall floor is 420 cm long and 300 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  30. 30.A hall floor is 320 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  31. 31.Two tanks hold 240 litres and 280 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  32. 32.A hall floor is 320 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  33. 33.Three temple bells ring every 6, 4 and 9 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 12 that leaves a remainder of 3 when divided by 5, 6 or 12.
  35. 35.Two tanks hold 200 litres and 360 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  36. 36.Zoya takes 30 seconds and Ananya takes 50 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.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?
  38. 38.Three temple bells ring every 8, 15 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.Three temple bells ring every 5, 12 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  40. 40.Three temple bells ring every 6, 5 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 40
  2. 40
  3. 40
  4. 34
  5. 60
  6. 15
  7. 32
  8. 120
  9. 72
  10. 20
  11. 40
  12. 91
  13. 30
  14. 360
  15. 5
  16. 24
  17. 40
  18. 14
  19. 120
  20. 60
  21. 40
  22. 21
  23. 216
  24. 120
  25. 180
  26. 123
  27. 40
  28. 120
  29. 35
  30. 24
  31. 40
  32. 40
  33. 36
  34. 63
  35. 40
  36. 150
  37. 10
  38. 120
  39. 60
  40. 30

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