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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 63 · 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.Three temple bells ring every 10, 4 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.A hall floor is 280 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  3. 3.Two tanks hold 105 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  4. 4.Rahul takes 40 seconds and Kavya 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?
  5. 5.Three temple bells ring every 6, 10 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.A hall floor is 175 cm long and 125 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  7. 7.Two tanks hold 10 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  8. 8.Three temple bells ring every 18, 4 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.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?
  10. 10.Two tanks hold 30 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  11. 11.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?
  12. 12.A hall floor is 175 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  13. 13.A hall floor is 140 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  14. 14.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?
  15. 15.A hall floor is 250 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  16. 16.Two tanks hold 80 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  17. 17.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 3, 15 or 4.
  18. 18.Two tanks hold 45 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  19. 19.Kabir takes 50 seconds and Sneha 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.Three temple bells ring every 10, 6 and 20 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 15 that leaves a remainder of 1 when divided by 3, 15 or 5.
  22. 22.Three temple bells ring every 5, 8 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.Three temple bells ring every 9, 18 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 10 or 3.
  25. 25.Three temple bells ring every 15, 4 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Two tanks hold 270 litres and 60 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, 5 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 12, 5 or 9.
  29. 29.Kavya takes 54 seconds and Nisha 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.Manav takes 40 seconds and Vivaan 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?
  31. 31.Kabir takes 30 seconds and Kavya 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?
  32. 32.Rahul takes 54 seconds and Meera 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?
  33. 33.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?
  34. 34.Three temple bells ring every 12, 30 and 24 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 10 that leaves a remainder of 2 when divided by 10, 5 or 3.
  36. 36.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?
  37. 37.Dev takes 30 seconds and Pooja 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?
  38. 38.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 12, 15 or 3.
  39. 39.Find the smallest number bigger than 6 that leaves a remainder of 2 when divided by 4, 6 or 3.
  40. 40.Two tanks hold 360 litres and 405 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?

Answer key

  1. 60
  2. 14
  3. 15
  4. 360
  5. 60
  6. 35
  7. 5
  8. 36
  9. 20
  10. 10
  11. 40
  12. 28
  13. 42
  14. 14
  15. 10
  16. 20
  17. 61
  18. 15
  19. 400
  20. 60
  21. 16
  22. 120
  23. 90
  24. 62
  25. 60
  26. 30
  27. 60
  28. 183
  29. 108
  30. 360
  31. 240
  32. 216
  33. 21
  34. 120
  35. 32
  36. 120
  37. 360
  38. 61
  39. 14
  40. 45

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