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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 567 · 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 180 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  2. 2.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 8 or 12.
  3. 3.Two tanks hold 100 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  4. 4.Three temple bells ring every 6, 5 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.Find the smallest number bigger than 10 that leaves a remainder of 4 when divided by 9, 5 or 10.
  6. 6.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?
  7. 7.Two tanks hold 30 litres and 70 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  8. 8.Two tanks hold 15 litres and 25 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  9. 9.Kabir takes 45 seconds and Ananya 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?
  10. 10.Three temple bells ring every 4, 6 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.Aditya takes 40 seconds and Rohan 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?
  12. 12.Three temple bells ring every 24, 10 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.Kavya takes 36 seconds and Karan 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?
  14. 14.Karan takes 36 seconds and Priya 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?
  15. 15.Three temple bells ring every 20, 6 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 15, 9 or 10.
  17. 17.A hall floor is 135 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  18. 18.Aarav takes 54 seconds and Tara 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?
  19. 19.Three temple bells ring every 4, 10 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.Find the smallest number bigger than 10 that leaves a remainder of 4 when divided by 8, 5 or 10.
  21. 21.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 6, 4 or 9.
  22. 22.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 10, 6 or 3.
  23. 23.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?
  24. 24.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 12, 15 or 10.
  25. 25.Diya takes 48 seconds and Ananya 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?
  26. 26.Nisha takes 80 seconds and Pooja 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?
  27. 27.Rahul takes 72 seconds and Zoya 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?
  28. 28.Isha takes 36 seconds and Meera 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?
  29. 29.Meera takes 48 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?
  30. 30.A hall floor is 175 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  31. 31.Two tanks hold 135 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  32. 32.Aditya takes 40 seconds and Manav 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?
  33. 33.Two tanks hold 20 litres and 25 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  34. 34.Two tanks hold 75 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  35. 35.Three temple bells ring every 12, 6 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.Three temple bells ring every 24, 4 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  37. 37.Ananya takes 36 seconds and Dev 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?
  38. 38.Sneha takes 45 seconds and Aarav 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?
  39. 39.Three temple bells ring every 12, 4 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  40. 40.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 10, 3 or 8.

Answer key

  1. 30
  2. 121
  3. 20
  4. 120
  5. 94
  6. 5
  7. 10
  8. 5
  9. 225
  10. 24
  11. 360
  12. 120
  13. 180
  14. 180
  15. 60
  16. 93
  17. 6
  18. 432
  19. 60
  20. 44
  21. 37
  22. 31
  23. 20
  24. 63
  25. 240
  26. 240
  27. 144
  28. 108
  29. 144
  30. 14
  31. 15
  32. 120
  33. 5
  34. 25
  35. 60
  36. 72
  37. 360
  38. 180
  39. 60
  40. 121

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