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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 246 · 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.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 3, 8 or 9.
  2. 2.Sneha takes 72 seconds and Meera 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?
  3. 3.Three temple bells ring every 15, 24 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.A hall floor is 140 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  5. 5.Three temple bells ring every 18, 5 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.Two tanks hold 280 litres and 80 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 5, 10 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.A hall floor is 120 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  9. 9.Sneha takes 50 seconds and Rohan 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?
  10. 10.Two tanks hold 225 litres and 315 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  11. 11.Zoya takes 60 seconds and Tara 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.Pooja takes 48 seconds and Kavya 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?
  13. 13.Two tanks hold 75 litres and 135 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.Two tanks hold 80 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  15. 15.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?
  16. 16.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 8, 3 or 5.
  17. 17.Three temple bells ring every 9, 10 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.Find the smallest number bigger than 15 that leaves a remainder of 5 when divided by 10, 9 or 15.
  19. 19.Three temple bells ring every 9, 24 and 6 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 2 when divided by 6, 3 or 15.
  21. 21.Two tanks hold 200 litres and 350 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  22. 22.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 4, 9 or 12.
  23. 23.Three temple bells ring every 6, 5 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 12, 9 or 4.
  25. 25.Kabir takes 45 seconds and Aarav 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?
  26. 26.Farhan takes 40 seconds and Rahul 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?
  27. 27.Two tanks hold 75 litres and 175 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  28. 28.Kavya takes 50 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?
  29. 29.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?
  30. 30.A hall floor is 420 cm long and 360 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  31. 31.Manav takes 90 seconds and Diya 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?
  32. 32.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 6 or 5.
  33. 33.Nisha takes 40 seconds and Ishaan 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?
  34. 34.Three temple bells ring every 15, 18 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.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?
  36. 36.Aarav takes 30 seconds and Kabir 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?
  37. 37.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 5, 10 or 9.
  38. 38.Three temple bells ring every 30, 20 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.Three temple bells ring every 5, 10 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  40. 40.Arjun takes 60 seconds and Farhan 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?

Answer key

  1. 73
  2. 144
  3. 120
  4. 14
  5. 90
  6. 40
  7. 20
  8. 30
  9. 200
  10. 45
  11. 240
  12. 240
  13. 15
  14. 40
  15. 72
  16. 122
  17. 90
  18. 95
  19. 72
  20. 32
  21. 50
  22. 37
  23. 30
  24. 39
  25. 90
  26. 200
  27. 25
  28. 150
  29. 45
  30. 42
  31. 180
  32. 61
  33. 120
  34. 90
  35. 42
  36. 240
  37. 92
  38. 120
  39. 30
  40. 180

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