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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 356 · 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.Three temple bells ring every 4, 10 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.A hall floor is 200 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  3. 3.Three temple bells ring every 15, 4 and 12 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 1 when divided by 5, 3 or 15.
  5. 5.A hall floor is 160 cm long and 140 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  6. 6.Two tanks hold 20 litres and 25 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  7. 7.Two tanks hold 150 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  8. 8.Two tanks hold 10 litres and 35 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  9. 9.A hall floor is 150 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  10. 10.Two tanks hold 70 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  11. 11.A hall floor is 140 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  12. 12.Two tanks hold 75 litres and 50 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  13. 13.Three temple bells ring every 15, 5 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.A hall floor is 280 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  15. 15.Three temple bells ring every 15, 9 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 4, 8 or 3.
  17. 17.Three temple bells ring every 20, 30 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.Nisha takes 40 seconds and Ananya 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?
  19. 19.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 5 or 3.
  20. 20.Two tanks hold 60 litres and 270 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 5, 30 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Three temple bells ring every 20, 12 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.Saanvi takes 72 seconds and Zoya 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?
  24. 24.Dev takes 30 seconds and Rahul 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?
  25. 25.Three temple bells ring every 15, 6 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 4, 6 or 10.
  27. 27.Three temple bells ring every 6, 9 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.Ishaan takes 45 seconds and Priya 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.Two tanks hold 35 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  30. 30.Rohan takes 45 seconds and Kabir 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?
  31. 31.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 10, 15 or 4.
  32. 32.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 3, 4 or 9.
  33. 33.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 15, 6 or 5.
  34. 34.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 3, 5 or 10.
  35. 35.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 5, 3 or 12.
  36. 36.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?
  37. 37.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?
  38. 38.Meera takes 75 seconds and Saanvi 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?
  39. 39.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 5, 15 or 3.
  40. 40.Two tanks hold 280 litres and 240 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?

Answer key

  1. 20
  2. 12
  3. 60
  4. 16
  5. 56
  6. 5
  7. 50
  8. 5
  9. 15
  10. 10
  11. 14
  12. 25
  13. 120
  14. 14
  15. 90
  16. 25
  17. 60
  18. 360
  19. 61
  20. 30
  21. 120
  22. 120
  23. 360
  24. 150
  25. 90
  26. 63
  27. 72
  28. 360
  29. 5
  30. 720
  31. 63
  32. 37
  33. 33
  34. 31
  35. 61
  36. 50
  37. 15
  38. 150
  39. 16
  40. 40

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