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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 409 · 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).

NameDateTime takenScore ___ / 40
  1. 1.A hall floor is 420 cm long and 360 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  2. 2.Two tanks hold 405 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  3. 3.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 12, 15 or 9.
  4. 4.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?
  5. 5.Two tanks hold 160 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  6. 6.Three temple bells ring every 24, 5 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.Three temple bells ring every 6, 5 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.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?
  9. 9.Three temple bells ring every 30, 8 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.Two tanks hold 350 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  11. 11.Two tanks hold 180 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  12. 12.A hall floor is 175 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  13. 13.Kavya takes 80 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?
  14. 14.A hall floor is 180 cm long and 135 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  15. 15.Three temple bells ring every 6, 20 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 3, 15 or 5.
  17. 17.Priya takes 80 seconds and Rahul 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?
  18. 18.Arjun takes 72 seconds and Saanvi 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.A hall floor is 90 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  20. 20.Three temple bells ring every 4, 15 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 4, 6 or 8.
  22. 22.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 4, 8 or 15.
  23. 23.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?
  24. 24.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 5, 9 or 15.
  25. 25.Two tanks hold 50 litres and 70 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  26. 26.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 3, 5 or 6.
  27. 27.Tara takes 45 seconds and Kabir 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?
  28. 28.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 4, 15 or 12.
  29. 29.A hall floor is 200 cm long and 160 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 5, 12 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 3 or 5.
  32. 32.Two tanks hold 60 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  33. 33.Two tanks hold 120 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  34. 34.Two tanks hold 150 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  35. 35.Three temple bells ring every 4, 9 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.Ananya takes 40 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?
  37. 37.Three temple bells ring every 15, 12 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.Two tanks hold 140 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  39. 39.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 9, 12 or 3.
  40. 40.A hall floor is 150 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?

Answer key

  1. 42
  2. 45
  3. 181
  4. 15
  5. 20
  6. 120
  7. 120
  8. 30
  9. 120
  10. 50
  11. 30
  12. 14
  13. 720
  14. 12
  15. 60
  16. 16
  17. 720
  18. 360
  19. 6
  20. 120
  21. 25
  22. 123
  23. 12
  24. 49
  25. 10
  26. 31
  27. 180
  28. 62
  29. 20
  30. 120
  31. 61
  32. 30
  33. 30
  34. 30
  35. 72
  36. 360
  37. 60
  38. 20
  39. 37
  40. 20

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