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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 131 · 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.Farhan 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?
  2. 2.Find the smallest number bigger than 6 that leaves a remainder of 2 when divided by 3, 6 or 5.
  3. 3.Find the smallest number bigger than 10 that leaves a remainder of 4 when divided by 10, 5 or 6.
  4. 4.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?
  5. 5.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 3, 10 or 15.
  6. 6.Two tanks hold 120 litres and 320 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  7. 7.Three temple bells ring every 30, 8 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.Two tanks hold 10 litres and 45 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 6, 15 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.Three temple bells ring every 4, 15 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.Three temple bells ring every 8, 6 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.Two tanks hold 225 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  13. 13.A hall floor is 240 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  14. 14.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 6, 4 or 15.
  15. 15.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 9 or 3.
  16. 16.Two tanks hold 50 litres and 30 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 12 that leaves a remainder of 1 when divided by 9, 5 or 12.
  18. 18.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?
  19. 19.Three temple bells ring every 30, 4 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.Two tanks hold 315 litres and 135 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  21. 21.Karan 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?
  22. 22.Three temple bells ring every 24, 10 and 4 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 12 that leaves a remainder of 1 when divided by 4, 12 or 6.
  24. 24.Three temple bells ring every 24, 18 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.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?
  26. 26.Two tanks hold 120 litres and 105 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  27. 27.Three temple bells ring every 9, 6 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.Three temple bells ring every 15, 6 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.A hall floor is 180 cm long and 150 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 250 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  31. 31.Dev takes 75 seconds and Manav 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?
  32. 32.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 5, 9 or 15.
  33. 33.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 3, 5 or 10.
  34. 34.Three temple bells ring every 18, 8 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.Two tanks hold 35 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  36. 36.Three temple bells ring every 4, 9 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  37. 37.Three temple bells ring every 6, 18 and 12 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 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  39. 39.Three temple bells ring every 6, 8 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  40. 40.Arjun takes 72 seconds and Aditya 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?

Answer key

  1. 240
  2. 32
  3. 34
  4. 12
  5. 31
  6. 40
  7. 120
  8. 5
  9. 30
  10. 60
  11. 24
  12. 45
  13. 24
  14. 61
  15. 46
  16. 10
  17. 181
  18. 15
  19. 60
  20. 45
  21. 150
  22. 120
  23. 13
  24. 72
  25. 56
  26. 15
  27. 90
  28. 60
  29. 30
  30. 35
  31. 150
  32. 46
  33. 32
  34. 72
  35. 5
  36. 36
  37. 36
  38. 21
  39. 24
  40. 360

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