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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 92 · 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 480 cm long and 420 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, 4 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.Three temple bells ring every 10, 5 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.Three temple bells ring every 15, 4 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.Three temple bells ring every 10, 4 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.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?
  7. 7.Two tanks hold 135 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  8. 8.A hall floor is 280 cm long and 240 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  9. 9.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 12, 9 or 15.
  10. 10.Pooja takes 48 seconds and Tara 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?
  11. 11.A hall floor is 140 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  12. 12.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 9, 15 or 4.
  13. 13.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 12, 5 or 6.
  14. 14.A hall floor is 280 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  15. 15.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?
  16. 16.Arjun takes 60 seconds and Aarav 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?
  17. 17.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?
  18. 18.Aditya takes 72 seconds and Diya 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?
  19. 19.Dev takes 72 seconds and Diya 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?
  20. 20.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 5, 15 or 4.
  21. 21.Aarav takes 60 seconds and Farhan 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?
  22. 22.Find the smallest number bigger than 15 that leaves a remainder of 5 when divided by 15, 8 or 10.
  23. 23.Two tanks hold 10 litres and 15 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  24. 24.Tara takes 30 seconds and Farhan 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?
  25. 25.Three temple bells ring every 6, 8 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Three temple bells ring every 5, 15 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.Diya takes 60 seconds and Kabir 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?
  28. 28.Two tanks hold 45 litres and 25 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  29. 29.Two tanks hold 30 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  30. 30.Two tanks hold 60 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  31. 31.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?
  32. 32.Three temple bells ring every 5, 30 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.Three temple bells ring every 12, 8 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 8 or 3.
  35. 35.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 3, 15 or 5.
  36. 36.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 4, 8 or 10.
  37. 37.Two tanks hold 175 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  38. 38.A hall floor is 250 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  39. 39.Farhan takes 72 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?
  40. 40.Three temple bells ring every 9, 8 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 56
  2. 60
  3. 20
  4. 120
  5. 60
  6. 21
  7. 15
  8. 42
  9. 181
  10. 240
  11. 14
  12. 183
  13. 63
  14. 21
  15. 6
  16. 180
  17. 120
  18. 360
  19. 216
  20. 63
  21. 180
  22. 125
  23. 5
  24. 360
  25. 120
  26. 30
  27. 300
  28. 5
  29. 15
  30. 20
  31. 10
  32. 90
  33. 72
  34. 25
  35. 16
  36. 42
  37. 25
  38. 10
  39. 360
  40. 72

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