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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 138 · 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.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 6, 8 or 4.
  2. 2.Rohan takes 54 seconds and Ishaan 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 450 litres and 250 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  4. 4.Ananya takes 50 seconds and Meera 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?
  5. 5.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?
  6. 6.Three temple bells ring every 6, 30 and 8 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 12 that leaves a remainder of 1 when divided by 9, 12 or 4.
  8. 8.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 9 or 10.
  9. 9.Three temple bells ring every 5, 30 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.Two tanks hold 270 litres and 315 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  11. 11.Two tanks hold 25 litres and 40 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 175 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  13. 13.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?
  14. 14.Tara takes 80 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?
  15. 15.Pooja takes 80 seconds and Diya 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?
  16. 16.Three temple bells ring every 4, 6 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.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?
  18. 18.A hall floor is 420 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  19. 19.Meera takes 40 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?
  20. 20.Arjun takes 80 seconds and Kavya 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?
  21. 21.Three temple bells ring every 30, 5 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Two tanks hold 60 litres and 270 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  23. 23.A hall floor is 80 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  24. 24.A hall floor is 200 cm long and 160 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  25. 25.Tara takes 30 seconds and Rohan 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?
  26. 26.Sneha takes 50 seconds and Vivaan 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?
  27. 27.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?
  28. 28.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 4, 5 or 8.
  29. 29.A hall floor is 160 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  30. 30.Three temple bells ring every 24, 20 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 10, 4 or 9.
  32. 32.A hall floor is 240 cm long and 210 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  33. 33.Pooja takes 36 seconds and Manav 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?
  34. 34.Manav takes 36 seconds and Arjun 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?
  35. 35.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 12, 6 or 4.
  36. 36.Three temple bells ring every 5, 12 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  37. 37.Three temple bells ring every 20, 5 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.Three temple bells ring every 5, 24 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.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?
  40. 40.Ishaan takes 36 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?

Answer key

  1. 26
  2. 216
  3. 50
  4. 450
  5. 72
  6. 120
  7. 37
  8. 182
  9. 120
  10. 45
  11. 5
  12. 14
  13. 14
  14. 720
  15. 720
  16. 60
  17. 21
  18. 14
  19. 240
  20. 400
  21. 90
  22. 30
  23. 12
  24. 20
  25. 150
  26. 400
  27. 12
  28. 42
  29. 12
  30. 120
  31. 183
  32. 56
  33. 108
  34. 108
  35. 15
  36. 60
  37. 60
  38. 120
  39. 25
  40. 180

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