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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 85 · 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 12 that leaves a remainder of 3 when divided by 4, 6 or 12.
  2. 2.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?
  3. 3.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?
  4. 4.Three temple bells ring every 15, 10 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.Find the smallest number bigger than 5 that leaves a remainder of 1 when divided by 5, 3 or 4.
  6. 6.Three temple bells ring every 15, 6 and 9 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 15 that leaves a remainder of 2 when divided by 3, 4 or 15.
  8. 8.Three temple bells ring every 8, 15 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.Two tanks hold 60 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  10. 10.Pooja takes 30 seconds and Karan 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?
  11. 11.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?
  12. 12.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 8, 3 or 5.
  13. 13.Kavya takes 40 seconds and Tara 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?
  14. 14.Two tanks hold 70 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  15. 15.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?
  16. 16.Meera takes 90 seconds and Kavya 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?
  17. 17.A hall floor is 100 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  18. 18.Karan takes 30 seconds and Saanvi 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?
  19. 19.Two tanks hold 60 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  20. 20.Find the smallest number bigger than 5 that leaves a remainder of 2 when divided by 4, 3 or 5.
  21. 21.Two tanks hold 30 litres and 135 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  22. 22.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 5, 6 or 15.
  23. 23.Three temple bells ring every 20, 10 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 4, 6 or 15.
  25. 25.A hall floor is 250 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  26. 26.Three temple bells ring every 12, 20 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.Three temple bells ring every 4, 6 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.Two tanks hold 40 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  29. 29.Three temple bells ring every 20, 24 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 5, 10 or 4.
  31. 31.Tara takes 40 seconds and Diya 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?
  32. 32.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?
  33. 33.A hall floor is 180 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  34. 34.Find the smallest number bigger than 12 that leaves a remainder of 4 when divided by 5, 12 or 6.
  35. 35.Meera takes 30 seconds and Rahul 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?
  36. 36.Two tanks hold 75 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  37. 37.Two tanks hold 30 litres and 70 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  38. 38.Priya takes 36 seconds and Manav 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?
  39. 39.Arjun takes 48 seconds and Isha 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?
  40. 40.Farhan takes 40 seconds and Karan 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?

Answer key

  1. 15
  2. 12
  3. 40
  4. 30
  5. 61
  6. 90
  7. 62
  8. 120
  9. 20
  10. 90
  11. 15
  12. 122
  13. 360
  14. 10
  15. 25
  16. 180
  17. 20
  18. 180
  19. 20
  20. 62
  21. 15
  22. 31
  23. 40
  24. 63
  25. 10
  26. 60
  27. 60
  28. 20
  29. 120
  30. 23
  31. 200
  32. 20
  33. 30
  34. 64
  35. 270
  36. 15
  37. 10
  38. 180
  39. 720
  40. 240

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