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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 384 · 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 120 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  2. 2.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 3, 9 or 4.
  3. 3.Tara takes 60 seconds and Zoya 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?
  4. 4.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?
  5. 5.Three temple bells ring every 4, 12 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.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?
  7. 7.Three temple bells ring every 10, 15 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.A hall floor is 210 cm long and 150 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 9 that leaves a remainder of 3 when divided by 6, 9 or 4.
  10. 10.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 4 or 9.
  11. 11.Three temple bells ring every 12, 9 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 3, 5 or 10.
  13. 13.Two tanks hold 25 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.Two tanks hold 80 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  15. 15.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?
  16. 16.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?
  17. 17.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 4, 5 or 10.
  18. 18.Priya takes 36 seconds and Aditya 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?
  19. 19.Three temple bells ring every 4, 30 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.A hall floor is 100 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  21. 21.Three temple bells ring every 24, 15 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Three temple bells ring every 10, 18 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.Two tanks hold 90 litres and 70 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  24. 24.A hall floor is 225 cm long and 135 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  25. 25.Two tanks hold 225 litres and 360 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  26. 26.A hall floor is 400 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  27. 27.Karan 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?
  28. 28.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 9, 12 or 3.
  29. 29.Two tanks hold 405 litres and 315 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  30. 30.Arjun takes 48 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?
  31. 31.Farhan takes 36 seconds and Tara 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.Find the smallest number bigger than 6 that leaves a remainder of 2 when divided by 4, 5 or 6.
  33. 33.A hall floor is 315 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  34. 34.Isha takes 75 seconds and Diya 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?
  35. 35.Find the smallest number bigger than 6 that leaves a remainder of 2 when divided by 5, 6 or 3.
  36. 36.Aarav takes 40 seconds and Pooja 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?
  37. 37.Three temple bells ring every 15, 5 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.A hall floor is 140 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  39. 39.Find the smallest number bigger than 9 that leaves a remainder of 3 when divided by 9, 4 or 6.
  40. 40.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 12, 9 or 4.

Answer key

  1. 6
  2. 37
  3. 300
  4. 56
  5. 24
  6. 120
  7. 60
  8. 35
  9. 39
  10. 181
  11. 36
  12. 32
  13. 5
  14. 20
  15. 24
  16. 15
  17. 22
  18. 180
  19. 120
  20. 12
  21. 120
  22. 90
  23. 10
  24. 15
  25. 45
  26. 24
  27. 180
  28. 38
  29. 45
  30. 240
  31. 108
  32. 62
  33. 28
  34. 150
  35. 32
  36. 360
  37. 90
  38. 35
  39. 39
  40. 39

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