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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 493 · 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, 30 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.Vivaan takes 36 seconds and Ananya 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.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 5, 12 or 4.
  4. 4.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 6, 15 or 3.
  5. 5.A hall floor is 210 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  6. 6.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?
  7. 7.A hall floor is 140 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  8. 8.Two tanks hold 360 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  9. 9.Three temple bells ring every 8, 4 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.Two tanks hold 20 litres and 45 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 40 litres and 100 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 100 litres and 450 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 5 that leaves a remainder of 2 when divided by 5, 4 or 3.
  14. 14.A hall floor is 150 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  15. 15.Find the smallest number bigger than 15 that leaves a remainder of 5 when divided by 12, 15 or 6.
  16. 16.Three temple bells ring every 18, 5 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 12, 10 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.A hall floor is 140 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  19. 19.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?
  20. 20.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?
  21. 21.Ishaan takes 50 seconds and Nisha 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?
  22. 22.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 10, 4 or 12.
  23. 23.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 3, 9 or 8.
  24. 24.Three temple bells ring every 30, 4 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.Three temple bells ring every 6, 20 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Two tanks hold 160 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  27. 27.Rohan takes 90 seconds and Arjun 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?
  28. 28.Two tanks hold 315 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  29. 29.A hall floor is 225 cm long and 180 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 5, 15 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.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?
  32. 32.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 4, 15 or 3.
  33. 33.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 5, 12 or 15.
  34. 34.Three temple bells ring every 12, 15 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.Zoya takes 40 seconds and Manav 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?
  36. 36.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 5 or 8.
  37. 37.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?
  38. 38.Isha takes 60 seconds and Vivaan 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?
  39. 39.A hall floor is 125 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  40. 40.Ananya takes 30 seconds and Zoya 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?

Answer key

  1. 60
  2. 180
  3. 63
  4. 31
  5. 28
  6. 60
  7. 21
  8. 40
  9. 120
  10. 5
  11. 20
  12. 50
  13. 62
  14. 15
  15. 65
  16. 90
  17. 60
  18. 14
  19. 20
  20. 42
  21. 400
  22. 61
  23. 74
  24. 60
  25. 60
  26. 40
  27. 180
  28. 45
  29. 20
  30. 60
  31. 56
  32. 62
  33. 62
  34. 60
  35. 240
  36. 122
  37. 6
  38. 300
  39. 10
  40. 180

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