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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 264 · 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 125 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  2. 2.Meera takes 40 seconds and Tara 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?
  3. 3.Three temple bells ring every 9, 15 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.Saanvi takes 40 seconds and Farhan 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?
  5. 5.A hall floor is 180 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  6. 6.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 10, 12 or 3.
  7. 7.Three temple bells ring every 4, 15 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 5, 6 or 12.
  9. 9.Three temple bells ring every 10, 9 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.Three temple bells ring every 8, 5 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.A hall floor is 320 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  12. 12.Two tanks hold 140 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  13. 13.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 4, 6 or 10.
  14. 14.Two tanks hold 120 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  15. 15.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 3, 15 or 6.
  16. 16.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 6, 3 or 10.
  17. 17.Find the smallest number bigger than 12 that leaves a remainder of 4 when divided by 5, 9 or 12.
  18. 18.Three temple bells ring every 24, 9 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Two tanks hold 45 litres and 105 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  20. 20.Arjun takes 54 seconds and Manav 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?
  21. 21.Two tanks hold 35 litres and 25 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  22. 22.Three temple bells ring every 6, 5 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.A hall floor is 300 cm long and 250 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  24. 24.Ananya takes 30 seconds and Manav 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?
  25. 25.Three temple bells ring every 12, 8 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Two tanks hold 315 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  27. 27.Two tanks hold 320 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  28. 28.Three temple bells ring every 9, 24 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Priya takes 48 seconds and Karan 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?
  30. 30.A hall floor is 240 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  31. 31.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 10, 5 or 15.
  32. 32.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 10, 5 or 4.
  33. 33.Farhan takes 50 seconds and Ananya 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?
  34. 34.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?
  35. 35.Two tanks hold 350 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  36. 36.Three temple bells ring every 12, 8 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  37. 37.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 3, 10 or 12.
  38. 38.A hall floor is 150 cm long and 125 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  39. 39.Three temple bells ring every 9, 5 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  40. 40.A hall floor is 140 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?

Answer key

  1. 25
  2. 360
  3. 90
  4. 120
  5. 6
  6. 61
  7. 60
  8. 61
  9. 90
  10. 120
  11. 24
  12. 20
  13. 61
  14. 30
  15. 31
  16. 31
  17. 184
  18. 72
  19. 15
  20. 270
  21. 5
  22. 120
  23. 30
  24. 90
  25. 24
  26. 45
  27. 40
  28. 72
  29. 144
  30. 12
  31. 33
  32. 23
  33. 200
  34. 40
  35. 50
  36. 24
  37. 61
  38. 30
  39. 90
  40. 42

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