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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 339 · 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 30, 8 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.Three temple bells ring every 5, 4 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.Find the smallest number bigger than 5 that leaves a remainder of 1 when divided by 4, 3 or 5.
  4. 4.Three temple bells ring every 4, 8 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.Three temple bells ring every 12, 5 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 8, 5 or 6.
  7. 7.Two tanks hold 350 litres and 300 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  8. 8.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 6, 8 or 15.
  9. 9.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?
  10. 10.Two tanks hold 50 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  11. 11.Three temple bells ring every 20, 15 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.A hall floor is 120 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  13. 13.Isha takes 36 seconds and Sneha 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?
  14. 14.A hall floor is 350 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  15. 15.Three temple bells ring every 20, 30 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.Three temple bells ring every 15, 4 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 5 or 12.
  18. 18.Two tanks hold 25 litres and 10 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  19. 19.Zoya takes 54 seconds and Diya 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?
  20. 20.Three temple bells ring every 5, 12 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.A hall floor is 315 cm long and 225 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  22. 22.Three temple bells ring every 12, 30 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  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.A hall floor is 150 cm long and 125 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  25. 25.Three temple bells ring every 12, 8 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Two tanks hold 250 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  27. 27.Two tanks hold 200 litres and 350 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  28. 28.A hall floor is 400 cm long and 350 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  29. 29.Ishaan takes 80 seconds and Karan 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.Two tanks hold 50 litres and 70 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  31. 31.Saanvi takes 54 seconds and Sneha 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?
  32. 32.Two tanks hold 40 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  33. 33.Zoya takes 72 seconds and Vivaan 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?
  34. 34.Three temple bells ring every 5, 8 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.Two tanks hold 150 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  36. 36.Vivaan takes 90 seconds and Manav 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?
  37. 37.Arjun takes 72 seconds and Diya 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?
  38. 38.Three temple bells ring every 24, 5 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.Two tanks hold 40 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  40. 40.Two tanks hold 400 litres and 350 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?

Answer key

  1. 120
  2. 60
  3. 61
  4. 24
  5. 120
  6. 122
  7. 50
  8. 124
  9. 6
  10. 10
  11. 60
  12. 12
  13. 180
  14. 21
  15. 60
  16. 60
  17. 62
  18. 5
  19. 216
  20. 60
  21. 35
  22. 60
  23. 14
  24. 30
  25. 120
  26. 50
  27. 50
  28. 56
  29. 720
  30. 10
  31. 270
  32. 10
  33. 360
  34. 120
  35. 30
  36. 450
  37. 144
  38. 120
  39. 10
  40. 50

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