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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 180 · 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).

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  1. 1.Two tanks hold 300 litres and 250 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  2. 2.Three temple bells ring every 30, 10 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.Three temple bells ring every 24, 12 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 5, 15 or 3.
  5. 5.Three temple bells ring every 6, 8 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 3, 5 or 12.
  7. 7.Three temple bells ring every 10, 8 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.A hall floor is 360 cm long and 225 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  9. 9.Three temple bells ring every 9, 6 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.Saanvi 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?
  11. 11.Two tanks hold 140 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  12. 12.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 10, 15 or 4.
  13. 13.Three temple bells ring every 10, 8 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.Kavya takes 50 seconds and Meera 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?
  15. 15.Farhan takes 36 seconds and Sneha 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 50 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  17. 17.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 3 or 9.
  18. 18.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?
  19. 19.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?
  20. 20.Two tanks hold 35 litres and 10 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  21. 21.Three temple bells ring every 6, 8 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 3, 15 or 9.
  23. 23.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 6, 8 or 3.
  24. 24.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 3 or 6.
  25. 25.Saanvi takes 60 seconds and Arjun 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?
  26. 26.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 9, 3 or 8.
  27. 27.Two tanks hold 60 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  28. 28.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?
  29. 29.Two tanks hold 400 litres and 450 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  30. 30.A hall floor is 60 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  31. 31.Ananya takes 54 seconds and Zoya 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?
  32. 32.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 4, 9 or 12.
  33. 33.Three temple bells ring every 15, 6 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.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?
  35. 35.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 6 or 5.
  36. 36.Two tanks hold 100 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  37. 37.A hall floor is 150 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  38. 38.Three temple bells ring every 8, 12 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.Arjun takes 45 seconds and Rahul 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?
  40. 40.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 3, 12 or 5.

Answer key

  1. 50
  2. 60
  3. 72
  4. 17
  5. 120
  6. 61
  7. 120
  8. 40
  9. 72
  10. 400
  11. 20
  12. 63
  13. 120
  14. 200
  15. 180
  16. 10
  17. 38
  18. 12
  19. 20
  20. 5
  21. 72
  22. 46
  23. 25
  24. 13
  25. 240
  26. 74
  27. 30
  28. 21
  29. 50
  30. 6
  31. 270
  32. 38
  33. 30
  34. 24
  35. 32
  36. 25
  37. 6
  38. 72
  39. 720
  40. 61

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