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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 61 · 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 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?
  2. 2.Three temple bells ring every 9, 10 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.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?
  4. 4.A hall floor is 315 cm long and 225 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  5. 5.Two tanks hold 105 litres and 135 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  6. 6.Saanvi takes 45 seconds and Tara takes 72 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.Meera takes 72 seconds and Rohan 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?
  8. 8.A hall floor is 200 cm long and 160 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  9. 9.Two tanks hold 150 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  10. 10.Three temple bells ring every 4, 15 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.Two tanks hold 80 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  12. 12.A hall floor is 175 cm long and 125 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  13. 13.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?
  14. 14.Three temple bells ring every 20, 24 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  15. 15.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?
  16. 16.A hall floor is 140 cm long and 60 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 9, 10 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 9, 4 or 6.
  19. 19.Three temple bells ring every 15, 30 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 8, 4 or 5.
  21. 21.Two tanks hold 25 litres and 35 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  22. 22.A hall floor is 350 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  23. 23.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?
  24. 24.Three temple bells ring every 4, 12 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.A hall floor is 280 cm long and 160 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  26. 26.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 3, 8 or 12.
  27. 27.Two tanks hold 40 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  28. 28.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 3, 8 or 9.
  29. 29.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?
  30. 30.Two tanks hold 125 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  31. 31.Find the smallest number bigger than 12 that leaves a remainder of 5 when divided by 12, 6 or 8.
  32. 32.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?
  33. 33.Two tanks hold 120 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  34. 34.Zoya takes 90 seconds and Sneha 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?
  35. 35.Two tanks hold 225 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  36. 36.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 4 or 12.
  37. 37.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?
  38. 38.Three temple bells ring every 5, 4 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.Aarav takes 75 seconds and Isha 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?
  40. 40.Find the smallest number bigger than 6 that leaves a remainder of 2 when divided by 6, 3 or 4.

Answer key

  1. 10
  2. 90
  3. 20
  4. 35
  5. 15
  6. 360
  7. 216
  8. 20
  9. 30
  10. 60
  11. 20
  12. 35
  13. 50
  14. 120
  15. 20
  16. 21
  17. 90
  18. 38
  19. 120
  20. 42
  21. 5
  22. 28
  23. 5
  24. 60
  25. 28
  26. 26
  27. 20
  28. 73
  29. 6
  30. 25
  31. 29
  32. 60
  33. 20
  34. 180
  35. 45
  36. 62
  37. 45
  38. 60
  39. 150
  40. 14

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