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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 558 · 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 60 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  2. 2.Three temple bells ring every 30, 9 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.Three temple bells ring every 12, 8 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.Three temple bells ring every 15, 30 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.Two tanks hold 60 litres and 135 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  6. 6.Two tanks hold 175 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  7. 7.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 4, 6 or 10.
  8. 8.A hall floor is 125 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  9. 9.Diya takes 45 seconds and Kabir 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?
  10. 10.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 10 or 3.
  11. 11.Two tanks hold 200 litres and 250 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  12. 12.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 10, 12 or 8.
  13. 13.Three temple bells ring every 20, 6 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.Manav takes 75 seconds and Diya 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?
  15. 15.Sneha takes 40 seconds and Aarav 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?
  16. 16.Nisha takes 45 seconds and Farhan 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?
  17. 17.A hall floor is 320 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  18. 18.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 5 or 6.
  19. 19.Ishaan takes 45 seconds and Arjun 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?
  20. 20.Dev takes 45 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?
  21. 21.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 10, 5 or 3.
  22. 22.Dev takes 75 seconds and Meera 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?
  23. 23.Three temple bells ring every 18, 12 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Two tanks hold 200 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  25. 25.Three temple bells ring every 6, 9 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  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.Sneha takes 90 seconds and Vivaan 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?
  28. 28.Two tanks hold 35 litres and 15 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  29. 29.Vivaan takes 90 seconds and Rohan 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?
  30. 30.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?
  31. 31.Three temple bells ring every 4, 6 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 10 or 4.
  33. 33.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 6 or 9.
  34. 34.A hall floor is 200 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  35. 35.Two tanks hold 320 litres and 360 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  36. 36.A hall floor is 150 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  37. 37.Three temple bells ring every 15, 24 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.Two tanks hold 100 litres and 160 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  39. 39.A hall floor is 140 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  40. 40.Three temple bells ring every 18, 10 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 30
  2. 90
  3. 24
  4. 60
  5. 15
  6. 25
  7. 61
  8. 20
  9. 90
  10. 32
  11. 50
  12. 123
  13. 60
  14. 300
  15. 360
  16. 180
  17. 40
  18. 62
  19. 180
  20. 90
  21. 31
  22. 600
  23. 36
  24. 40
  25. 36
  26. 5
  27. 180
  28. 5
  29. 180
  30. 50
  31. 60
  32. 62
  33. 92
  34. 15
  35. 40
  36. 15
  37. 120
  38. 20
  39. 35
  40. 90

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