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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 37 · 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 10, 8 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.Meera takes 90 seconds and Arjun 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?
  3. 3.Pooja takes 60 seconds and Dev 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?
  4. 4.A hall floor is 175 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  5. 5.Find the smallest number bigger than 5 that leaves a remainder of 2 when divided by 4, 3 or 5.
  6. 6.Three temple bells ring every 9, 12 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.Rahul takes 48 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?
  8. 8.Ananya takes 45 seconds and Ishaan 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?
  9. 9.Two tanks hold 40 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  10. 10.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 5 or 8.
  11. 11.Ananya takes 36 seconds and Aarav 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?
  12. 12.Dev takes 80 seconds and Pooja 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?
  13. 13.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 10, 9 or 3.
  14. 14.Three temple bells ring every 20, 8 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  15. 15.Two tanks hold 40 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  16. 16.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 6, 8 or 3.
  17. 17.A hall floor is 100 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  18. 18.A hall floor is 240 cm long and 200 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 24, 5 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.Two tanks hold 60 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  21. 21.A hall floor is 225 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  22. 22.Vivaan takes 50 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?
  23. 23.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 6, 15 or 8.
  24. 24.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 5, 4 or 12.
  25. 25.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?
  26. 26.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 8, 9 or 12.
  27. 27.Arjun takes 48 seconds and Karan 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?
  28. 28.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 10, 4 or 5.
  29. 29.A hall floor is 140 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  30. 30.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?
  31. 31.A hall floor is 175 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  32. 32.A hall floor is 280 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  33. 33.Meera takes 45 seconds and Zoya 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?
  34. 34.Rahul takes 54 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?
  35. 35.A hall floor is 200 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  36. 36.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 3, 4 or 12.
  37. 37.Two tanks hold 80 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  38. 38.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 3, 9 or 15.
  39. 39.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?
  40. 40.Three temple bells ring every 4, 30 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 40
  2. 360
  3. 360
  4. 42
  5. 62
  6. 72
  7. 432
  8. 450
  9. 20
  10. 122
  11. 144
  12. 400
  13. 91
  14. 120
  15. 10
  16. 25
  17. 15
  18. 30
  19. 120
  20. 15
  21. 10
  22. 150
  23. 121
  24. 61
  25. 10
  26. 73
  27. 240
  28. 22
  29. 35
  30. 40
  31. 21
  32. 21
  33. 360
  34. 270
  35. 12
  36. 13
  37. 40
  38. 47
  39. 28
  40. 60

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