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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 461 · 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 8, 30 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.Three temple bells ring every 9, 18 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.Tara takes 48 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?
  4. 4.Two tanks hold 35 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  5. 5.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 5, 12 or 4.
  6. 6.Three temple bells ring every 30, 5 and 9 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, 24 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 15, 6 or 4.
  9. 9.Two tanks hold 40 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 15 that leaves a remainder of 3 when divided by 15, 6 or 12.
  11. 11.Two tanks hold 240 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.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?
  13. 13.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 6, 3 or 8.
  14. 14.Meera takes 80 seconds and Isha 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?
  15. 15.Two tanks hold 300 litres and 250 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  16. 16.Meera takes 72 seconds and Dev 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?
  17. 17.Find the smallest number bigger than 9 that leaves a remainder of 3 when divided by 6, 9 or 5.
  18. 18.Three temple bells ring every 15, 5 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.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?
  20. 20.Three temple bells ring every 15, 10 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.Two tanks hold 80 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  22. 22.A hall floor is 300 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  23. 23.Sneha takes 60 seconds and Meera 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?
  24. 24.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?
  25. 25.Three temple bells ring every 24, 9 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Two tanks hold 10 litres and 15 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 15 that leaves a remainder of 1 when divided by 10, 15 or 5.
  28. 28.Sneha takes 72 seconds and Rohan 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?
  29. 29.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 6, 10 or 9.
  30. 30.Vivaan takes 72 seconds and Zoya 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?
  31. 31.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?
  32. 32.Two tanks hold 25 litres and 35 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 15 that leaves a remainder of 1 when divided by 4, 5 or 15.
  34. 34.Two tanks hold 60 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  35. 35.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 3, 15 or 12.
  36. 36.Dev takes 90 seconds and Tara 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?
  37. 37.Three temple bells ring every 15, 4 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.A hall floor is 360 cm long and 135 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  39. 39.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 4, 8 or 6.
  40. 40.Two tanks hold 150 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?

Answer key

  1. 120
  2. 90
  3. 144
  4. 5
  5. 61
  6. 90
  7. 120
  8. 63
  9. 5
  10. 63
  11. 30
  12. 90
  13. 25
  14. 400
  15. 50
  16. 360
  17. 93
  18. 30
  19. 14
  20. 60
  21. 40
  22. 10
  23. 360
  24. 45
  25. 72
  26. 5
  27. 31
  28. 360
  29. 92
  30. 360
  31. 45
  32. 5
  33. 61
  34. 20
  35. 62
  36. 180
  37. 120
  38. 24
  39. 25
  40. 30

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