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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 291 · 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 80 litres and 140 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, 12 or 5.
  3. 3.Pooja takes 60 seconds and Aditya 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?
  4. 4.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 9, 4 or 15.
  5. 5.Sneha takes 45 seconds and Meera 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?
  6. 6.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 5, 3 or 10.
  7. 7.Three temple bells ring every 24, 30 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.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?
  9. 9.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 5, 8 or 4.
  10. 10.Aarav takes 90 seconds and Tara 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?
  11. 11.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 4, 8 or 10.
  12. 12.Aarav takes 72 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?
  13. 13.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 12, 6 or 15.
  14. 14.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?
  15. 15.Two tanks hold 60 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  16. 16.Aditya takes 90 seconds and Priya 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?
  17. 17.Two tanks hold 400 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  18. 18.Two tanks hold 45 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  19. 19.Ishaan takes 36 seconds and Karan 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?
  20. 20.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 6, 3 or 10.
  21. 21.Three temple bells ring every 20, 4 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 4, 15 or 6.
  23. 23.A hall floor is 420 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  24. 24.Two tanks hold 320 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  25. 25.Two tanks hold 105 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  26. 26.Meera takes 75 seconds and Rohan 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?
  27. 27.Ananya takes 30 seconds and Nisha 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.Three temple bells ring every 5, 8 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 4 or 9.
  30. 30.Three temple bells ring every 4, 20 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.Three temple bells ring every 6, 10 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.Three temple bells ring every 10, 5 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.Two tanks hold 30 litres and 20 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 30 litres and 45 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 4, 8 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.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?
  37. 37.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 3, 8 or 10.
  38. 38.Karan takes 60 seconds and Saanvi 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?
  39. 39.Three temple bells ring every 6, 9 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  40. 40.Two tanks hold 200 litres and 175 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?

Answer key

  1. 20
  2. 61
  3. 180
  4. 182
  5. 450
  6. 31
  7. 120
  8. 14
  9. 42
  10. 270
  11. 43
  12. 144
  13. 63
  14. 5
  15. 20
  16. 450
  17. 50
  18. 15
  19. 720
  20. 31
  21. 60
  22. 62
  23. 14
  24. 40
  25. 15
  26. 450
  27. 240
  28. 40
  29. 37
  30. 60
  31. 30
  32. 20
  33. 10
  34. 15
  35. 120
  36. 6
  37. 121
  38. 300
  39. 90
  40. 25

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