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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 35 · 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 48 seconds and Aditya 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?
  2. 2.Three temple bells ring every 8, 4 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.A hall floor is 315 cm long and 135 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  4. 4.A hall floor is 120 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  5. 5.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?
  6. 6.A hall floor is 250 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  7. 7.Three temple bells ring every 4, 12 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.A hall floor is 200 cm long and 125 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 3 when divided by 10, 12 or 5.
  10. 10.A hall floor is 240 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 160 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  12. 12.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 9, 4 or 5.
  13. 13.Two tanks hold 120 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.Nisha takes 30 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?
  15. 15.Sneha takes 60 seconds and Pooja 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?
  16. 16.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 9, 12 or 10.
  17. 17.Manav takes 48 seconds and Aditya 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?
  18. 18.Meera takes 72 seconds and Diya 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?
  19. 19.Three temple bells ring every 9, 5 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.Ishaan takes 80 seconds and Ananya 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?
  21. 21.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 9, 4 or 3.
  22. 22.A hall floor is 360 cm long and 225 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  23. 23.Find the smallest number bigger than 15 that leaves a remainder of 5 when divided by 12, 15 or 9.
  24. 24.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?
  25. 25.A hall floor is 200 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  26. 26.Manav takes 90 seconds and Vivaan 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?
  27. 27.Three temple bells ring every 9, 6 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 3, 12 or 4.
  29. 29.Two tanks hold 100 litres and 160 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  30. 30.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 4, 8 or 15.
  31. 31.A hall floor is 100 cm long and 40 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 15, 24 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.Two tanks hold 20 litres and 70 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  34. 34.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?
  35. 35.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 12, 15 or 3.
  36. 36.Zoya takes 30 seconds and Aditya 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?
  37. 37.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 4, 3 or 10.
  38. 38.Three temple bells ring every 8, 6 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.Rahul takes 54 seconds and Kabir 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?
  40. 40.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 9, 6 or 3.

Answer key

  1. 432
  2. 24
  3. 21
  4. 6
  5. 36
  6. 20
  7. 36
  8. 40
  9. 63
  10. 24
  11. 40
  12. 181
  13. 30
  14. 270
  15. 180
  16. 181
  17. 144
  18. 360
  19. 90
  20. 240
  21. 37
  22. 40
  23. 185
  24. 14
  25. 15
  26. 360
  27. 90
  28. 13
  29. 20
  30. 122
  31. 10
  32. 120
  33. 10
  34. 6
  35. 61
  36. 270
  37. 62
  38. 72
  39. 108
  40. 19

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