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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 45 · 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.A hall floor is 200 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  2. 2.Three temple bells ring every 10, 8 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.Two tanks hold 180 litres and 135 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  4. 4.Find the smallest number bigger than 8 that leaves a remainder of 3 when divided by 8, 5 or 4.
  5. 5.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 4, 3 or 15.
  6. 6.Three temple bells ring every 12, 10 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.Three temple bells ring every 5, 30 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 9, 6 or 15.
  9. 9.Aditya takes 50 seconds and Diya 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?
  10. 10.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?
  11. 11.Kavya takes 80 seconds and Aarav 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?
  12. 12.A hall floor is 140 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  13. 13.Three temple bells ring every 5, 4 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.Aarav takes 36 seconds and Nisha 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?
  15. 15.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 4, 12 or 8.
  16. 16.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 10, 6 or 4.
  17. 17.Two tanks hold 240 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  18. 18.Three temple bells ring every 6, 18 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.A hall floor is 480 cm long and 420 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  20. 20.Two tanks hold 20 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  21. 21.Ananya takes 40 seconds and Priya 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?
  22. 22.Three temple bells ring every 24, 8 and 20 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 10 that leaves a remainder of 1 when divided by 9, 10 or 5.
  24. 24.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 8, 6 or 5.
  25. 25.A hall floor is 125 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  26. 26.Three temple bells ring every 6, 10 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 9, 3 or 12.
  28. 28.Find the smallest number bigger than 6 that leaves a remainder of 2 when divided by 6, 4 or 5.
  29. 29.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?
  30. 30.Three temple bells ring every 4, 10 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.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?
  32. 32.Saanvi takes 36 seconds and Dev 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?
  33. 33.Three temple bells ring every 15, 24 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.Kabir takes 90 seconds and Sneha 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?
  35. 35.A hall floor is 240 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  36. 36.Three temple bells ring every 4, 15 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  37. 37.Two tanks hold 160 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  38. 38.Two tanks hold 320 litres and 280 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  39. 39.Three temple bells ring every 18, 8 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  40. 40.Two tanks hold 100 litres and 450 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?

Answer key

  1. 24
  2. 120
  3. 45
  4. 43
  5. 61
  6. 120
  7. 60
  8. 92
  9. 150
  10. 6
  11. 720
  12. 21
  13. 60
  14. 144
  15. 25
  16. 62
  17. 40
  18. 36
  19. 56
  20. 10
  21. 360
  22. 120
  23. 91
  24. 121
  25. 10
  26. 30
  27. 38
  28. 62
  29. 40
  30. 120
  31. 120
  32. 720
  33. 120
  34. 180
  35. 40
  36. 60
  37. 20
  38. 40
  39. 72
  40. 50

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