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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 1 · 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 160 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  2. 2.A hall floor is 160 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  3. 3.Two tanks hold 200 litres and 360 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  4. 4.Three temple bells ring every 9, 8 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.Three temple bells ring every 4, 6 and 9 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 6, 4 or 8.
  7. 7.Ananya takes 45 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?
  8. 8.Three temple bells ring every 4, 15 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 12, 9 or 4.
  10. 10.Pooja takes 48 seconds and Arjun 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?
  11. 11.Three temple bells ring every 5, 10 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.Three temple bells ring every 10, 4 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.Arjun takes 54 seconds and Kabir 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?
  14. 14.Three temple bells ring every 24, 20 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  15. 15.Arjun takes 45 seconds and Ishaan 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?
  16. 16.Ananya takes 50 seconds and Saanvi 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?
  17. 17.Two tanks hold 135 litres and 75 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 270 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  19. 19.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 4, 10 or 3.
  20. 20.Two tanks hold 200 litres and 125 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  21. 21.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?
  22. 22.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 3, 10 or 9.
  23. 23.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 10, 15 or 3.
  24. 24.Two tanks hold 30 litres and 135 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  25. 25.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?
  26. 26.Kavya takes 30 seconds and Saanvi 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?
  27. 27.Three temple bells ring every 30, 24 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.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?
  29. 29.Three temple bells ring every 6, 20 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.A hall floor is 120 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  31. 31.Aarav takes 45 seconds and Dev 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?
  32. 32.Three temple bells ring every 4, 15 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.A hall floor is 420 cm long and 240 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 30, 15 and 9 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 15 that leaves a remainder of 1 when divided by 4, 15 or 6.
  36. 36.A hall floor is 350 cm long and 300 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 4, 6 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.Find the smallest number bigger than 6 that leaves a remainder of 2 when divided by 4, 6 or 3.
  39. 39.Ananya takes 72 seconds and Sneha 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?
  40. 40.A hall floor is 360 cm long and 315 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?

Answer key

  1. 40
  2. 40
  3. 40
  4. 72
  5. 36
  6. 26
  7. 180
  8. 60
  9. 39
  10. 720
  11. 90
  12. 60
  13. 216
  14. 120
  15. 360
  16. 400
  17. 15
  18. 30
  19. 61
  20. 25
  21. 21
  22. 91
  23. 31
  24. 15
  25. 28
  26. 120
  27. 120
  28. 20
  29. 120
  30. 30
  31. 450
  32. 120
  33. 28
  34. 90
  35. 61
  36. 42
  37. 60
  38. 14
  39. 360
  40. 56

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