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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 382 · 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.Arjun takes 54 seconds and Pooja 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?
  2. 2.Zoya takes 54 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?
  3. 3.Two tanks hold 105 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  4. 4.Three temple bells ring every 15, 6 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.Meera takes 90 seconds and Kabir 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?
  6. 6.Find the smallest number bigger than 6 that leaves a remainder of 2 when divided by 4, 5 or 6.
  7. 7.Three temple bells ring every 6, 9 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.Two tanks hold 90 litres and 70 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 4, 6 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.Aarav takes 80 seconds and Ananya 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?
  11. 11.Kabir takes 30 seconds and Rahul 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?
  12. 12.Three temple bells ring every 9, 6 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.Farhan takes 80 seconds and Priya 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?
  14. 14.Arjun takes 45 seconds and Kabir 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?
  15. 15.A hall floor is 160 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  16. 16.Two tanks hold 90 litres and 405 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 9 that leaves a remainder of 3 when divided by 5, 4 or 9.
  18. 18.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 4, 9 or 8.
  19. 19.Three temple bells ring every 4, 5 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.Find the smallest number bigger than 15 that leaves a remainder of 5 when divided by 15, 9 or 6.
  21. 21.A hall floor is 180 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  22. 22.Two tanks hold 10 litres and 25 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  23. 23.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?
  24. 24.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 10 or 9.
  25. 25.Priya takes 45 seconds and Farhan 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?
  26. 26.Three temple bells ring every 4, 30 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.Three temple bells ring every 18, 9 and 5 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, 4 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 4, 12 or 5.
  30. 30.Two tanks hold 160 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  31. 31.Three temple bells ring every 20, 6 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.Priya takes 30 seconds and Kavya 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?
  33. 33.Two tanks hold 160 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  34. 34.Tara takes 30 seconds and Priya 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?
  35. 35.Three temple bells ring every 10, 20 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.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?
  37. 37.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?
  38. 38.Three temple bells ring every 30, 5 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.Two tanks hold 200 litres and 120 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 175 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?

Answer key

  1. 108
  2. 270
  3. 15
  4. 120
  5. 270
  6. 62
  7. 90
  8. 10
  9. 60
  10. 720
  11. 180
  12. 72
  13. 240
  14. 360
  15. 24
  16. 45
  17. 183
  18. 73
  19. 60
  20. 95
  21. 6
  22. 5
  23. 15
  24. 181
  25. 270
  26. 60
  27. 90
  28. 60
  29. 63
  30. 40
  31. 60
  32. 150
  33. 20
  34. 90
  35. 60
  36. 36
  37. 10
  38. 60
  39. 40
  40. 42

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