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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 9 · 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 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.Three temple bells ring every 20, 8 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.Three temple bells ring every 20, 6 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 6, 15 or 5.
  5. 5.Two tanks hold 180 litres and 210 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  6. 6.Three temple bells ring every 9, 15 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.Ananya takes 40 seconds and Aarav 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?
  8. 8.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?
  9. 9.Find the smallest number bigger than 12 that leaves a remainder of 5 when divided by 12, 9 or 6.
  10. 10.Rahul takes 48 seconds and Kabir 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?
  11. 11.Priya takes 50 seconds and Tara 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?
  12. 12.Three temple bells ring every 9, 12 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.Two tanks hold 315 litres and 225 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 320 cm long and 120 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 24, 30 and 15 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 15 that leaves a remainder of 3 when divided by 15, 10 or 4.
  17. 17.Two tanks hold 240 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  18. 18.Three temple bells ring every 5, 15 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Sneha takes 30 seconds and Farhan 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?
  20. 20.Three temple bells ring every 12, 4 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.Three temple bells ring every 15, 12 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Two tanks hold 225 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  23. 23.Three temple bells ring every 30, 15 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Two tanks hold 450 litres and 350 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  25. 25.Meera takes 45 seconds and Priya 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?
  26. 26.Three temple bells ring every 18, 4 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.Two tanks hold 45 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  28. 28.Three temple bells ring every 20, 24 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Priya takes 60 seconds and Meera 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?
  30. 30.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 15, 8 or 12.
  31. 31.Three temple bells ring every 8, 30 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.Saanvi takes 30 seconds and Aditya 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?
  33. 33.Two tanks hold 125 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  34. 34.Three temple bells ring every 8, 15 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.Three temple bells ring every 8, 5 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.Zoya takes 60 seconds and Aditya 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?
  37. 37.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 3, 12 or 8.
  38. 38.A hall floor is 135 cm long and 90 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 10 that leaves a remainder of 1 when divided by 10, 4 or 5.
  40. 40.Nisha takes 72 seconds and Rohan 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?

Answer key

  1. 120
  2. 120
  3. 60
  4. 33
  5. 30
  6. 45
  7. 200
  8. 72
  9. 41
  10. 240
  11. 450
  12. 36
  13. 45
  14. 24
  15. 120
  16. 63
  17. 40
  18. 120
  19. 360
  20. 60
  21. 60
  22. 25
  23. 60
  24. 50
  25. 720
  26. 36
  27. 15
  28. 120
  29. 120
  30. 123
  31. 120
  32. 270
  33. 25
  34. 120
  35. 120
  36. 540
  37. 25
  38. 6
  39. 21
  40. 216

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