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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 336 · 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 5, 4 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.Two tanks hold 320 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  3. 3.Two tanks hold 50 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  4. 4.Vivaan takes 60 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?
  5. 5.Three temple bells ring every 4, 24 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.Three temple bells ring every 10, 24 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 3, 6 or 15.
  8. 8.A hall floor is 280 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  9. 9.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 4, 12 or 9.
  10. 10.Dev takes 54 seconds and Saanvi 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?
  11. 11.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?
  12. 12.Ananya takes 40 seconds and Karan 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?
  13. 13.Three temple bells ring every 30, 6 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.Three temple bells ring every 8, 20 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  15. 15.Three temple bells ring every 12, 24 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.Three temple bells ring every 10, 30 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.A hall floor is 200 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  18. 18.A hall floor is 100 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  19. 19.Two tanks hold 270 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  20. 20.Two tanks hold 50 litres and 125 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  21. 21.Three temple bells ring every 18, 8 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.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?
  23. 23.Find the smallest number bigger than 12 that leaves a remainder of 5 when divided by 6, 10 or 12.
  24. 24.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 4, 10 or 3.
  25. 25.Zoya takes 40 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?
  26. 26.Manav takes 40 seconds and Rohan 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?
  27. 27.Three temple bells ring every 5, 10 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.Sneha takes 30 seconds and Aditya 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?
  29. 29.Ananya takes 90 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?
  30. 30.A hall floor is 315 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  31. 31.A hall floor is 350 cm long and 300 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  32. 32.Three temple bells ring every 10, 5 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.Three temple bells ring every 10, 5 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.A hall floor is 150 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  35. 35.Three temple bells ring every 8, 9 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.Nisha takes 60 seconds and Kavya 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?
  37. 37.A hall floor is 140 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  38. 38.Two tanks hold 320 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  39. 39.A hall floor is 160 cm long and 140 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  40. 40.Saanvi takes 90 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?

Answer key

  1. 120
  2. 40
  3. 10
  4. 180
  5. 120
  6. 120
  7. 31
  8. 14
  9. 37
  10. 432
  11. 5
  12. 120
  13. 90
  14. 40
  15. 120
  16. 60
  17. 24
  18. 12
  19. 30
  20. 25
  21. 72
  22. 40
  23. 65
  24. 62
  25. 360
  26. 240
  27. 90
  28. 150
  29. 720
  30. 28
  31. 42
  32. 90
  33. 120
  34. 6
  35. 72
  36. 360
  37. 28
  38. 40
  39. 56
  40. 720

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