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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 287 · 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.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 4, 15 or 9.
  2. 2.A hall floor is 175 cm long and 125 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  3. 3.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 4, 5 or 15.
  4. 4.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?
  5. 5.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?
  6. 6.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 6, 10 or 3.
  7. 7.A hall floor is 120 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  8. 8.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?
  9. 9.Three temple bells ring every 15, 8 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.Two tanks hold 120 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  11. 11.Three temple bells ring every 15, 24 and 30 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 15 that leaves a remainder of 1 when divided by 3, 15 or 9.
  13. 13.Two tanks hold 20 litres and 15 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.Three temple bells ring every 15, 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 10, 24 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.Two tanks hold 240 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  17. 17.Two tanks hold 315 litres and 405 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  18. 18.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?
  19. 19.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 10, 9 or 15.
  20. 20.Three temple bells ring every 12, 30 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.A hall floor is 75 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  22. 22.Tara takes 45 seconds and Farhan 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?
  23. 23.Two tanks hold 70 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  24. 24.Three temple bells ring every 12, 5 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.Two tanks hold 60 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.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?
  27. 27.Three temple bells ring every 10, 15 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.A hall floor is 100 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  29. 29.A hall floor is 315 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  30. 30.A hall floor is 350 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  31. 31.Karan takes 48 seconds and Priya 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?
  32. 32.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?
  33. 33.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 10, 3 or 5.
  34. 34.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?
  35. 35.Karan takes 30 seconds and Aditya 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?
  36. 36.Karan takes 50 seconds and Kabir 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?
  37. 37.Karan takes 50 seconds and Nisha 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?
  38. 38.Find the smallest number bigger than 15 that leaves a remainder of 5 when divided by 12, 9 or 15.
  39. 39.Two tanks hold 75 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  40. 40.A hall floor is 100 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?

Answer key

  1. 183
  2. 35
  3. 62
  4. 10
  5. 28
  6. 31
  7. 30
  8. 20
  9. 120
  10. 20
  11. 120
  12. 46
  13. 5
  14. 60
  15. 120
  16. 30
  17. 45
  18. 21
  19. 91
  20. 60
  21. 6
  22. 90
  23. 10
  24. 60
  25. 15
  26. 21
  27. 30
  28. 10
  29. 14
  30. 14
  31. 720
  32. 30
  33. 32
  34. 42
  35. 150
  36. 150
  37. 450
  38. 185
  39. 15
  40. 15

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