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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 176 · 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 240 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  2. 2.A hall floor is 160 cm long and 140 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  3. 3.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?
  4. 4.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 9, 4 or 15.
  5. 5.Two tanks hold 45 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  6. 6.A hall floor is 150 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  7. 7.Kavya takes 48 seconds and Meera 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.Three temple bells ring every 4, 24 and 5 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 2 when divided by 3, 12 or 6.
  10. 10.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 3 or 6.
  11. 11.Two tanks hold 45 litres and 105 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  12. 12.Two tanks hold 120 litres and 320 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  13. 13.Two tanks hold 50 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.Tara takes 36 seconds and Farhan 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?
  15. 15.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 5, 3 or 10.
  16. 16.A hall floor is 300 cm long and 240 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  17. 17.Arjun takes 60 seconds and Isha 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?
  18. 18.Three temple bells ring every 20, 8 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 9, 10 or 4.
  20. 20.Two tanks hold 100 litres and 140 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  21. 21.Three temple bells ring every 30, 24 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 5, 12 or 4.
  23. 23.Dev takes 40 seconds and Ananya 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?
  24. 24.Arjun takes 36 seconds and Isha 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?
  25. 25.Two tanks hold 30 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  26. 26.Three temple bells ring every 8, 30 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.A hall floor is 180 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  28. 28.Two tanks hold 80 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  29. 29.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 5, 9 or 4.
  30. 30.A hall floor is 80 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  31. 31.Diya takes 48 seconds and Ananya 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?
  32. 32.Three temple bells ring every 8, 4 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.Nisha takes 90 seconds and Tara 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?
  34. 34.Three temple bells ring every 12, 5 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.Three temple bells ring every 24, 10 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.Isha takes 45 seconds and Vivaan 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?
  37. 37.Two tanks hold 175 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  38. 38.Three temple bells ring every 24, 12 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.Three temple bells ring every 30, 6 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  40. 40.Three temple bells ring every 9, 24 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 30
  2. 56
  3. 21
  4. 183
  5. 15
  6. 15
  7. 720
  8. 120
  9. 14
  10. 32
  11. 15
  12. 40
  13. 10
  14. 180
  15. 31
  16. 20
  17. 180
  18. 120
  19. 181
  20. 20
  21. 120
  22. 63
  23. 360
  24. 180
  25. 15
  26. 120
  27. 6
  28. 10
  29. 182
  30. 12
  31. 432
  32. 120
  33. 720
  34. 60
  35. 120
  36. 180
  37. 25
  38. 120
  39. 60
  40. 72

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