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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 420 · 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.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?
  2. 2.Isha takes 30 seconds and Kavya 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.Two tanks hold 225 litres and 135 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  4. 4.Manav takes 36 seconds and Aarav 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?
  5. 5.A hall floor is 400 cm long and 350 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  6. 6.Two tanks hold 50 litres and 70 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  7. 7.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 3, 10 or 8.
  8. 8.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 6, 4 or 9.
  9. 9.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?
  10. 10.Three temple bells ring every 5, 6 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.Manav takes 60 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?
  12. 12.Three temple bells ring every 30, 8 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.Sneha takes 40 seconds and Aditya 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?
  14. 14.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?
  15. 15.Two tanks hold 70 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  16. 16.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?
  17. 17.Three temple bells ring every 20, 8 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.Three temple bells ring every 6, 8 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 10, 3 or 5.
  20. 20.Find the smallest number bigger than 10 that leaves a remainder of 4 when divided by 8, 5 or 10.
  21. 21.Ishaan takes 50 seconds and Farhan 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.Three temple bells ring every 5, 6 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 6, 9 or 8.
  24. 24.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 10, 6 or 3.
  25. 25.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?
  26. 26.Two tanks hold 225 litres and 175 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  27. 27.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 8 or 6.
  28. 28.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 10, 9 or 5.
  29. 29.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?
  30. 30.Ananya takes 90 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?
  31. 31.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 9 or 8.
  32. 32.Two tanks hold 90 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  33. 33.Two tanks hold 50 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  34. 34.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 9, 6 or 5.
  35. 35.Ishaan takes 75 seconds and Aarav 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?
  36. 36.Tara takes 54 seconds and Aditya 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?
  37. 37.Three temple bells ring every 12, 4 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.Three temple bells ring every 30, 24 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.A hall floor is 100 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  40. 40.A hall floor is 160 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?

Answer key

  1. 35
  2. 90
  3. 45
  4. 180
  5. 56
  6. 10
  7. 121
  8. 38
  9. 6
  10. 30
  11. 180
  12. 120
  13. 240
  14. 35
  15. 10
  16. 21
  17. 40
  18. 24
  19. 31
  20. 44
  21. 400
  22. 60
  23. 74
  24. 32
  25. 14
  26. 25
  27. 122
  28. 92
  29. 40
  30. 450
  31. 74
  32. 30
  33. 10
  34. 92
  35. 300
  36. 270
  37. 60
  38. 120
  39. 12
  40. 40

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