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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 515 · 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.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 3, 4 or 10.
  2. 2.Two tanks hold 150 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  3. 3.A hall floor is 225 cm long and 180 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 12 that leaves a remainder of 1 when divided by 12, 6 or 9.
  5. 5.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 8, 6 or 10.
  6. 6.Two tanks hold 150 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  7. 7.Meera takes 40 seconds and Dev 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?
  8. 8.A hall floor is 360 cm long and 315 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  9. 9.Three temple bells ring every 9, 24 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.Two tanks hold 60 litres and 70 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  11. 11.Two tanks hold 405 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  12. 12.Three temple bells ring every 15, 9 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.Two tanks hold 210 litres and 270 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.Two tanks hold 40 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  15. 15.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?
  16. 16.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 15, 12 or 4.
  17. 17.Two tanks hold 360 litres and 280 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  18. 18.Three temple bells ring every 10, 4 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Manav takes 45 seconds and Priya 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?
  20. 20.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?
  21. 21.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?
  22. 22.Three temple bells ring every 24, 5 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.Three temple bells ring every 30, 8 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.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?
  25. 25.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 4 or 8.
  26. 26.A hall floor is 280 cm long and 240 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  27. 27.Arjun takes 72 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?
  28. 28.Two tanks hold 35 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  29. 29.Tara takes 36 seconds and Meera 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?
  30. 30.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?
  31. 31.A hall floor is 140 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  32. 32.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?
  33. 33.Three temple bells ring every 12, 15 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.A hall floor is 160 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  35. 35.Three temple bells ring every 6, 8 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.Isha takes 90 seconds and Arjun 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?
  37. 37.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 9, 4 or 5.
  38. 38.Three temple bells ring every 12, 20 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.Three temple bells ring every 6, 18 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  40. 40.Two tanks hold 120 litres and 270 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?

Answer key

  1. 62
  2. 50
  3. 20
  4. 37
  5. 122
  6. 30
  7. 240
  8. 56
  9. 72
  10. 10
  11. 45
  12. 45
  13. 30
  14. 10
  15. 30
  16. 63
  17. 40
  18. 40
  19. 180
  20. 30
  21. 24
  22. 120
  23. 120
  24. 20
  25. 122
  26. 42
  27. 360
  28. 5
  29. 180
  30. 5
  31. 14
  32. 15
  33. 60
  34. 12
  35. 120
  36. 360
  37. 181
  38. 120
  39. 90
  40. 30

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