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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 307 · 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 18, 5 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.Zoya takes 45 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?
  3. 3.Two tanks hold 120 litres and 100 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 5, 6 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.Pooja takes 36 seconds and Arjun 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?
  6. 6.Manav takes 30 seconds and Pooja 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?
  7. 7.Three temple bells ring every 4, 30 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.Three temple bells ring every 4, 6 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.Three temple bells ring every 6, 24 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.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?
  11. 11.A hall floor is 420 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  12. 12.A hall floor is 75 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  13. 13.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 5, 3 or 12.
  14. 14.Two tanks hold 20 litres and 35 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  15. 15.Rahul takes 30 seconds and Saanvi 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?
  16. 16.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 3, 15 or 5.
  17. 17.Two tanks hold 200 litres and 250 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  18. 18.A hall floor is 225 cm long and 135 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  19. 19.Three temple bells ring every 8, 24 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.Arjun takes 50 seconds and Priya 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?
  21. 21.Three temple bells ring every 24, 5 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Two tanks hold 90 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.Rahul takes 72 seconds and Zoya 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?
  24. 24.Kabir takes 40 seconds and Kavya 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?
  25. 25.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 3, 6 or 15.
  26. 26.Two tanks hold 75 litres and 125 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  27. 27.Rahul takes 48 seconds and Sneha 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?
  28. 28.A hall floor is 480 cm long and 420 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  29. 29.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?
  30. 30.Three temple bells ring every 9, 4 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.Three temple bells ring every 6, 8 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.A hall floor is 125 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  33. 33.Pooja takes 54 seconds and Aditya 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.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 8, 6 or 10.
  35. 35.A hall floor is 175 cm long and 125 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  36. 36.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 8, 4 or 3.
  37. 37.Two tanks hold 60 litres and 210 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 140 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  39. 39.Dev takes 60 seconds and Diya 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?
  40. 40.Two tanks hold 20 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. 90
  2. 360
  3. 20
  4. 60
  5. 720
  6. 240
  7. 60
  8. 60
  9. 120
  10. 45
  11. 21
  12. 6
  13. 61
  14. 5
  15. 150
  16. 17
  17. 50
  18. 15
  19. 120
  20. 300
  21. 120
  22. 10
  23. 360
  24. 120
  25. 32
  26. 25
  27. 240
  28. 56
  29. 72
  30. 36
  31. 120
  32. 20
  33. 540
  34. 121
  35. 35
  36. 26
  37. 30
  38. 14
  39. 240
  40. 10

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