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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 410 · 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.A hall floor is 480 cm long and 300 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  2. 2.Three temple bells ring every 8, 6 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.Two tanks hold 35 litres and 15 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 175 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  5. 5.Three temple bells ring every 15, 5 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.Two tanks hold 30 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  7. 7.Three temple bells ring every 20, 6 and 4 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 10 that leaves a remainder of 2 when divided by 10, 9 or 3.
  9. 9.Three temple bells ring every 10, 30 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.Two tanks hold 225 litres and 315 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  11. 11.Find the smallest number bigger than 15 that leaves a remainder of 7 when divided by 12, 15 or 9.
  12. 12.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 5, 10 or 4.
  13. 13.Two tanks hold 50 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 3, 8 or 10.
  15. 15.Rohan takes 80 seconds and Pooja 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?
  16. 16.A hall floor is 160 cm long and 100 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 15, 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 15 that leaves a remainder of 1 when divided by 15, 3 or 12.
  19. 19.Two tanks hold 75 litres and 30 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 25 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.Rohan takes 30 seconds and Diya 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?
  22. 22.Three temple bells ring every 24, 8 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.A hall floor is 100 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  24. 24.Three temple bells ring every 24, 15 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.Two tanks hold 90 litres and 210 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  26. 26.A hall floor is 150 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  27. 27.Two tanks hold 210 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.Aarav takes 80 seconds and Kabir 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?
  29. 29.Ishaan 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?
  30. 30.Tara takes 40 seconds and Meera 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?
  31. 31.A hall floor is 360 cm long and 135 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  32. 32.Three temple bells ring every 12, 20 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.Three temple bells ring every 20, 5 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.A hall floor is 210 cm long and 60 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 1 when divided by 15, 10 or 3.
  36. 36.Two tanks hold 50 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  37. 37.Kavya takes 80 seconds and Ishaan 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?
  38. 38.Aarav takes 30 seconds and Ishaan 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?
  39. 39.Two tanks hold 30 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  40. 40.Three temple bells ring every 30, 6 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 40
  2. 120
  3. 5
  4. 42
  5. 60
  6. 10
  7. 60
  8. 92
  9. 60
  10. 45
  11. 187
  12. 22
  13. 25
  14. 121
  15. 240
  16. 40
  17. 30
  18. 61
  19. 15
  20. 5
  21. 150
  22. 72
  23. 15
  24. 120
  25. 30
  26. 20
  27. 30
  28. 720
  29. 90
  30. 120
  31. 24
  32. 60
  33. 60
  34. 14
  35. 31
  36. 10
  37. 720
  38. 240
  39. 10
  40. 90

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