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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 202 · 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.Diya takes 48 seconds and Nisha 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?
  2. 2.Aarav takes 45 seconds and Saanvi takes 75 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.Kavya takes 75 seconds and Saanvi 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?
  4. 4.A hall floor is 480 cm long and 300 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  5. 5.Two tanks hold 175 litres and 125 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 4, 24 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.Farhan takes 45 seconds and Diya 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?
  8. 8.A hall floor is 125 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  9. 9.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?
  10. 10.A hall floor is 120 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  11. 11.Two tanks hold 30 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  12. 12.Two tanks hold 80 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  13. 13.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 5, 3 or 9.
  14. 14.Sneha takes 60 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?
  15. 15.Three temple bells ring every 30, 12 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.Three temple bells ring every 6, 15 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.Three temple bells ring every 10, 8 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.A hall floor is 150 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  19. 19.Kavya takes 75 seconds and Sneha 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?
  20. 20.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 10, 6 or 4.
  21. 21.Three temple bells ring every 10, 9 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.A hall floor is 140 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  23. 23.Aditya takes 80 seconds and Manav 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?
  24. 24.A hall floor is 420 cm long and 300 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  25. 25.Tara takes 60 seconds and Aditya 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?
  26. 26.Two tanks hold 90 litres and 70 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  27. 27.Two tanks hold 40 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.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?
  29. 29.Find the smallest number bigger than 15 that leaves a remainder of 8 when divided by 15, 9 or 10.
  30. 30.Three temple bells ring every 18, 10 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.Three temple bells ring every 12, 4 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.Three temple bells ring every 18, 15 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 5, 8 or 4.
  34. 34.Ananya takes 60 seconds and Aarav 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?
  35. 35.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?
  36. 36.Three temple bells ring every 5, 6 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  37. 37.Three temple bells ring every 8, 6 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.A hall floor is 350 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  39. 39.A hall floor is 400 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  40. 40.A hall floor is 180 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?

Answer key

  1. 720
  2. 225
  3. 300
  4. 40
  5. 25
  6. 120
  7. 270
  8. 15
  9. 42
  10. 12
  11. 10
  12. 10
  13. 46
  14. 240
  15. 60
  16. 30
  17. 40
  18. 10
  19. 600
  20. 62
  21. 90
  22. 42
  23. 240
  24. 35
  25. 120
  26. 10
  27. 10
  28. 30
  29. 98
  30. 90
  31. 36
  32. 90
  33. 42
  34. 180
  35. 60
  36. 90
  37. 120
  38. 21
  39. 24
  40. 6

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