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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 297 · 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 175 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  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.Three temple bells ring every 8, 20 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.Three temple bells ring every 18, 6 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.A hall floor is 100 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  6. 6.A hall floor is 420 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  7. 7.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 3, 5 or 6.
  8. 8.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 5 or 4.
  9. 9.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?
  10. 10.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 9, 3 or 10.
  11. 11.Aditya takes 80 seconds and Saanvi 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?
  12. 12.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 6, 3 or 9.
  13. 13.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 9, 4 or 3.
  14. 14.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 5, 6 or 15.
  15. 15.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 5, 4 or 8.
  16. 16.Find the smallest number bigger than 15 that leaves a remainder of 5 when divided by 10, 8 or 15.
  17. 17.Three temple bells ring every 20, 30 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.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?
  19. 19.Priya takes 36 seconds and Arjun 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.Farhan takes 30 seconds and Ananya 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?
  21. 21.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?
  22. 22.Three temple bells ring every 9, 24 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 6, 15 or 4.
  24. 24.Two tanks hold 50 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  25. 25.Three temple bells ring every 5, 24 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Three temple bells ring every 30, 12 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.Two tanks hold 50 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  28. 28.Three temple bells ring every 8, 9 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Tara takes 48 seconds and Meera 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?
  30. 30.Three temple bells ring every 24, 15 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.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?
  32. 32.Three temple bells ring every 10, 18 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.Three temple bells ring every 10, 12 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.Diya takes 36 seconds and Aditya takes 40 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.Two tanks hold 150 litres and 240 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  36. 36.Two tanks hold 90 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  37. 37.Three temple bells ring every 9, 8 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.Aarav takes 60 seconds and Ishaan 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?
  39. 39.Two tanks hold 135 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  40. 40.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 4, 9 or 5.

Answer key

  1. 14
  2. 35
  3. 120
  4. 72
  5. 20
  6. 14
  7. 31
  8. 61
  9. 15
  10. 92
  11. 240
  12. 20
  13. 38
  14. 34
  15. 41
  16. 125
  17. 60
  18. 6
  19. 108
  20. 150
  21. 14
  22. 72
  23. 62
  24. 10
  25. 120
  26. 60
  27. 10
  28. 72
  29. 240
  30. 120
  31. 20
  32. 90
  33. 60
  34. 360
  35. 30
  36. 15
  37. 72
  38. 180
  39. 45
  40. 181

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