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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 387 · 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).

NameDateTime takenScore ___ / 40
  1. 1.Two tanks hold 30 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  2. 2.Manav takes 50 seconds and Dev takes 75 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?
  3. 3.Two tanks hold 225 litres and 50 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 200 cm long and 175 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  5. 5.Diya takes 45 seconds and Arjun 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?
  6. 6.Three temple bells ring every 6, 8 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.Rohan takes 60 seconds and Kavya takes 75 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.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 15, 8 or 10.
  9. 9.Three temple bells ring every 5, 15 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 10, 4 or 5.
  11. 11.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 4, 9 or 12.
  12. 12.Kabir takes 80 seconds and Rahul 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?
  13. 13.Find the smallest number bigger than 10 that leaves a remainder of 4 when divided by 6, 10 or 5.
  14. 14.Three temple bells ring every 20, 6 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  15. 15.Two tanks hold 250 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  16. 16.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 8, 12 or 5.
  17. 17.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 5, 4 or 9.
  18. 18.Three temple bells ring every 8, 6 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.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?
  20. 20.Two tanks hold 140 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  21. 21.Find the smallest number bigger than 12 that leaves a remainder of 7 when divided by 8, 12 or 9.
  22. 22.A hall floor is 420 cm long and 240 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  23. 23.Three temple bells ring every 12, 15 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Two tanks hold 320 litres and 280 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  25. 25.A hall floor is 150 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  26. 26.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?
  27. 27.Three temple bells ring every 30, 15 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.Three temple bells ring every 10, 4 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Two tanks hold 225 litres and 405 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  30. 30.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 9, 8 or 6.
  31. 31.Two tanks hold 80 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.Two tanks hold 350 litres and 300 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  33. 33.A hall floor is 60 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  34. 34.Find the smallest number bigger than 12 that leaves a remainder of 7 when divided by 10, 9 or 12.
  35. 35.Ananya takes 80 seconds and Priya 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?
  36. 36.Two tanks hold 25 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  37. 37.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?
  38. 38.Three temple bells ring every 8, 9 and 18 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 12 that leaves a remainder of 2 when divided by 12, 4 or 3.
  40. 40.Karan takes 40 seconds and Farhan 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?

Answer key

  1. 10
  2. 150
  3. 25
  4. 56
  5. 720
  6. 72
  7. 300
  8. 124
  9. 90
  10. 21
  11. 37
  12. 720
  13. 34
  14. 60
  15. 50
  16. 121
  17. 181
  18. 72
  19. 14
  20. 20
  21. 79
  22. 28
  23. 120
  24. 40
  25. 20
  26. 5
  27. 60
  28. 60
  29. 45
  30. 73
  31. 40
  32. 50
  33. 6
  34. 187
  35. 720
  36. 5
  37. 72
  38. 72
  39. 14
  40. 240

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