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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 415 · 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 140 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  2. 2.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?
  3. 3.Two tanks hold 30 litres and 70 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, 18 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.Isha 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?
  6. 6.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 9, 8 or 6.
  7. 7.Rahul takes 36 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?
  8. 8.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?
  9. 9.Three temple bells ring every 30, 5 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.Three temple bells ring every 30, 8 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 10 or 4.
  12. 12.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?
  13. 13.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?
  14. 14.Three temple bells ring every 24, 12 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  15. 15.Three temple bells ring every 6, 4 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.Saanvi takes 90 seconds and Dev 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?
  17. 17.Two tanks hold 320 litres and 120 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 60 litres and 105 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  19. 19.A hall floor is 280 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  20. 20.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 9, 5 or 12.
  21. 21.Vivaan takes 30 seconds and Kavya takes 54 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.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 9, 10 or 4.
  23. 23.A hall floor is 300 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 210 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  25. 25.Two tanks hold 350 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  26. 26.Nisha takes 75 seconds and Tara 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?
  27. 27.Three temple bells ring every 15, 5 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 350 cm long and 300 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 8, 4 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.A hall floor is 210 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  31. 31.Three temple bells ring every 5, 10 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.Two tanks hold 150 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  33. 33.Tara takes 90 seconds and Isha 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?
  34. 34.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?
  35. 35.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 9, 6 or 8.
  36. 36.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 9, 4 or 12.
  37. 37.Priya takes 36 seconds and Saanvi 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?
  38. 38.Two tanks hold 120 litres and 135 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  39. 39.Vivaan takes 54 seconds and Zoya 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?
  40. 40.Saanvi takes 75 seconds and Rahul 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?

Answer key

  1. 28
  2. 21
  3. 10
  4. 72
  5. 300
  6. 74
  7. 180
  8. 30
  9. 90
  10. 120
  11. 61
  12. 28
  13. 60
  14. 120
  15. 60
  16. 360
  17. 40
  18. 15
  19. 35
  20. 183
  21. 270
  22. 181
  23. 10
  24. 21
  25. 50
  26. 225
  27. 60
  28. 42
  29. 24
  30. 14
  31. 40
  32. 50
  33. 180
  34. 6
  35. 73
  36. 38
  37. 180
  38. 15
  39. 216
  40. 150

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