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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 49 · 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.Rohan takes 80 seconds and Dev takes 90 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.Aditya takes 30 seconds and Manav 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?
  3. 3.Two tanks hold 80 litres and 70 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  4. 4.A hall floor is 315 cm long and 270 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  5. 5.Ananya takes 72 seconds and Saanvi 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?
  6. 6.Two tanks hold 225 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  7. 7.Meera takes 45 seconds and Diya 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.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?
  9. 9.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?
  10. 10.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?
  11. 11.Two tanks hold 140 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  12. 12.A hall floor is 100 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  13. 13.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?
  14. 14.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 8, 15 or 6.
  15. 15.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 5, 6 or 15.
  16. 16.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?
  17. 17.Two tanks hold 50 litres and 225 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 240 cm long and 150 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 5, 15 and 9 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 10 that leaves a remainder of 4 when divided by 8, 5 or 10.
  21. 21.A hall floor is 315 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  22. 22.Zoya takes 36 seconds and Diya 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?
  23. 23.Two tanks hold 315 litres and 270 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  24. 24.Manav takes 45 seconds and Meera 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?
  25. 25.Two tanks hold 35 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  26. 26.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 8, 12 or 6.
  27. 27.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?
  28. 28.Two tanks hold 200 litres and 320 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  29. 29.Two tanks hold 150 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  30. 30.Two tanks hold 40 litres and 70 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  31. 31.Two tanks hold 50 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  32. 32.Diya takes 75 seconds and Meera 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?
  33. 33.Aditya takes 50 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?
  34. 34.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 10, 5 or 6.
  35. 35.Vivaan takes 45 seconds and Priya 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?
  36. 36.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?
  37. 37.Two tanks hold 135 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  38. 38.Three temple bells ring every 20, 12 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.Three temple bells ring every 6, 15 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  40. 40.Three temple bells ring every 4, 24 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 720
  2. 90
  3. 10
  4. 42
  5. 360
  6. 45
  7. 450
  8. 10
  9. 14
  10. 21
  11. 20
  12. 20
  13. 50
  14. 122
  15. 33
  16. 56
  17. 25
  18. 40
  19. 45
  20. 44
  21. 14
  22. 180
  23. 45
  24. 180
  25. 5
  26. 27
  27. 120
  28. 40
  29. 50
  30. 10
  31. 10
  32. 150
  33. 150
  34. 33
  35. 180
  36. 30
  37. 15
  38. 60
  39. 60
  40. 120

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