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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 26 · 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 15 that leaves a remainder of 1 when divided by 9, 12 or 15.
  2. 2.Two tanks hold 360 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  3. 3.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 10, 6 or 5.
  4. 4.Two tanks hold 270 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  5. 5.A hall floor is 90 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  6. 6.Saanvi takes 48 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?
  7. 7.Three temple bells ring every 15, 8 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.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?
  9. 9.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 10, 8 or 5.
  10. 10.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 4, 15 or 3.
  11. 11.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 10, 3 or 4.
  12. 12.Karan takes 40 seconds and Meera takes 75 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.A hall floor is 125 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  14. 14.A hall floor is 280 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  15. 15.Ishaan takes 48 seconds and Rohan 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?
  16. 16.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?
  17. 17.Two tanks hold 250 litres and 350 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  18. 18.A hall floor is 225 cm long and 135 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  19. 19.Two tanks hold 70 litres and 60 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 12 that leaves a remainder of 2 when divided by 9, 4 or 12.
  21. 21.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?
  22. 22.Three temple bells ring every 24, 4 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.Three temple bells ring every 15, 5 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Two tanks hold 140 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  25. 25.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 5, 15 or 12.
  26. 26.Three temple bells ring every 18, 24 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.Meera takes 90 seconds and Rohan 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.A hall floor is 480 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  29. 29.Saanvi takes 80 seconds and Pooja 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?
  30. 30.Two tanks hold 25 litres and 15 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  31. 31.Three temple bells ring every 24, 6 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 5, 3 or 12.
  33. 33.A hall floor is 140 cm long and 80 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 1 when divided by 9, 10 or 12.
  35. 35.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 3, 15 or 8.
  36. 36.Two tanks hold 40 litres and 25 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  37. 37.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 5, 12 or 4.
  38. 38.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 4, 8 or 5.
  39. 39.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 6, 5 or 10.
  40. 40.Two tanks hold 360 litres and 315 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?

Answer key

  1. 181
  2. 45
  3. 32
  4. 30
  5. 6
  6. 144
  7. 120
  8. 30
  9. 42
  10. 61
  11. 61
  12. 600
  13. 20
  14. 35
  15. 240
  16. 20
  17. 50
  18. 15
  19. 10
  20. 38
  21. 21
  22. 120
  23. 30
  24. 20
  25. 63
  26. 72
  27. 720
  28. 24
  29. 720
  30. 5
  31. 72
  32. 61
  33. 28
  34. 181
  35. 122
  36. 5
  37. 61
  38. 42
  39. 33
  40. 45

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