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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 98 · 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.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 5, 15 or 6.
  2. 2.Three temple bells ring every 18, 4 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.Rohan takes 36 seconds and Kabir 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?
  4. 4.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?
  5. 5.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 8, 5 or 15.
  6. 6.Three temple bells ring every 4, 20 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.Two tanks hold 270 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  8. 8.Manav takes 36 seconds and Ananya 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?
  9. 9.Two tanks hold 90 litres and 105 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  10. 10.Two tanks hold 10 litres and 25 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  11. 11.Aditya 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?
  12. 12.Ishaan takes 90 seconds and Farhan 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?
  13. 13.Two tanks hold 10 litres and 15 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 6, 3 or 12.
  15. 15.Three temple bells ring every 20, 24 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.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?
  17. 17.Three temple bells ring every 18, 5 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 5, 4 or 10.
  19. 19.Two tanks hold 60 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  20. 20.Three temple bells ring every 4, 5 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 10, 5 or 8.
  22. 22.Three temple bells ring every 10, 4 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.Two tanks hold 90 litres and 20 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 160 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  25. 25.Sneha takes 45 seconds and Aditya 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.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?
  27. 27.Three temple bells ring every 6, 18 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.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?
  29. 29.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 8, 3 or 10.
  30. 30.A hall floor is 300 cm long and 240 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  31. 31.Two tanks hold 80 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  32. 32.Find the smallest number bigger than 15 that leaves a remainder of 5 when divided by 6, 15 or 8.
  33. 33.Kabir takes 50 seconds and Dev 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?
  34. 34.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?
  35. 35.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 6, 4 or 9.
  36. 36.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?
  37. 37.Find the smallest number bigger than 8 that leaves a remainder of 3 when divided by 8, 4 or 5.
  38. 38.Three temple bells ring every 8, 24 and 5 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, 15 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  40. 40.Two tanks hold 100 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?

Answer key

  1. 31
  2. 72
  3. 108
  4. 15
  5. 124
  6. 60
  7. 30
  8. 360
  9. 15
  10. 5
  11. 720
  12. 360
  13. 5
  14. 13
  15. 120
  16. 36
  17. 90
  18. 21
  19. 15
  20. 60
  21. 43
  22. 20
  23. 10
  24. 20
  25. 180
  26. 15
  27. 90
  28. 21
  29. 121
  30. 20
  31. 20
  32. 125
  33. 450
  34. 40
  35. 37
  36. 20
  37. 43
  38. 120
  39. 30
  40. 25

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