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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 496 · 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.Three temple bells ring every 24, 20 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.Two tanks hold 105 litres and 60 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 15, 10 or 5.
  4. 4.A hall floor is 150 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  5. 5.Ananya takes 90 seconds and Manav 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?
  6. 6.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 8, 3 or 15.
  7. 7.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 9, 4 or 10.
  8. 8.Three temple bells ring every 18, 6 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 6, 5 or 15.
  10. 10.Rahul takes 60 seconds and Arjun 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?
  11. 11.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 10, 8 or 4.
  12. 12.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 5, 15 or 9.
  13. 13.Two tanks hold 60 litres and 270 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.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?
  15. 15.Three temple bells ring every 4, 8 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.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?
  17. 17.Three temple bells ring every 12, 8 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.Three temple bells ring every 12, 30 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Dev takes 40 seconds and Vivaan 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?
  20. 20.Three temple bells ring every 18, 8 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.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?
  22. 22.Three temple bells ring every 5, 9 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.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?
  24. 24.Two tanks hold 35 litres and 15 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  25. 25.A hall floor is 280 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  26. 26.Two tanks hold 60 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  27. 27.Find the smallest number bigger than 5 that leaves a remainder of 2 when divided by 3, 5 or 4.
  28. 28.Three temple bells ring every 10, 6 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.A hall floor is 200 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  30. 30.Two tanks hold 30 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  31. 31.Find the smallest number bigger than 15 that leaves a remainder of 5 when divided by 10, 8 or 15.
  32. 32.Three temple bells ring every 5, 8 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.A hall floor is 80 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  34. 34.Saanvi takes 90 seconds and Sneha 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?
  35. 35.Zoya takes 36 seconds and Ananya 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?
  36. 36.Dev takes 50 seconds and Kavya 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?
  37. 37.Two tanks hold 30 litres and 25 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  38. 38.A hall floor is 400 cm long and 250 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  39. 39.Two tanks hold 90 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  40. 40.Tara takes 60 seconds and Manav 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?

Answer key

  1. 120
  2. 15
  3. 31
  4. 10
  5. 360
  6. 122
  7. 183
  8. 36
  9. 31
  10. 240
  11. 41
  12. 48
  13. 30
  14. 20
  15. 72
  16. 15
  17. 72
  18. 60
  19. 360
  20. 72
  21. 20
  22. 90
  23. 60
  24. 5
  25. 14
  26. 15
  27. 62
  28. 30
  29. 10
  30. 15
  31. 125
  32. 120
  33. 12
  34. 720
  35. 180
  36. 400
  37. 5
  38. 40
  39. 10
  40. 360

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