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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 550 · 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 45 litres and 35 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  2. 2.Two tanks hold 140 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  3. 3.Karan takes 60 seconds and Meera 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?
  4. 4.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 9, 4 or 15.
  5. 5.Three temple bells ring every 18, 12 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.Zoya takes 60 seconds and Saanvi 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?
  7. 7.A hall floor is 180 cm long and 135 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  8. 8.Three temple bells ring every 9, 6 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.Three temple bells ring every 10, 6 and 5 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 12 that leaves a remainder of 4 when divided by 6, 12 or 9.
  11. 11.Three temple bells ring every 5, 6 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.Two tanks hold 75 litres and 105 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  13. 13.Priya takes 40 seconds and Rohan 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?
  14. 14.Two tanks hold 225 litres and 135 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 420 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  16. 16.Karan takes 50 seconds and Rahul 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?
  17. 17.Dev takes 75 seconds and Arjun 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?
  18. 18.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 10, 5 or 4.
  19. 19.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 5, 8 or 15.
  20. 20.Two tanks hold 60 litres and 270 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  21. 21.Three temple bells ring every 4, 15 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Three temple bells ring every 15, 18 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 4, 5 or 15.
  24. 24.Three temple bells ring every 15, 20 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.Arjun takes 40 seconds and Vivaan 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?
  26. 26.Karan takes 90 seconds and Kabir 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?
  27. 27.Find the smallest number bigger than 12 that leaves a remainder of 7 when divided by 10, 12 or 9.
  28. 28.Two tanks hold 60 litres and 140 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  29. 29.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 9, 10 or 5.
  30. 30.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?
  31. 31.Three temple bells ring every 12, 30 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.Sneha takes 75 seconds and Farhan 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?
  33. 33.A hall floor is 210 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  34. 34.Three temple bells ring every 8, 20 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 4, 3 or 6.
  36. 36.Two tanks hold 175 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  37. 37.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 8, 3 or 9.
  38. 38.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?
  39. 39.Nisha takes 72 seconds and Vivaan 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?
  40. 40.Two tanks hold 50 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?

Answer key

  1. 5
  2. 20
  3. 180
  4. 181
  5. 72
  6. 180
  7. 12
  8. 90
  9. 30
  10. 40
  11. 30
  12. 15
  13. 600
  14. 45
  15. 21
  16. 450
  17. 150
  18. 22
  19. 121
  20. 30
  21. 60
  22. 90
  23. 61
  24. 60
  25. 240
  26. 180
  27. 187
  28. 20
  29. 92
  30. 20
  31. 60
  32. 300
  33. 14
  34. 120
  35. 13
  36. 25
  37. 74
  38. 15
  39. 144
  40. 10

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