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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 197 · 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 80 litres and 90 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 6, 18 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.A hall floor is 350 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  4. 4.Two tanks hold 200 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  5. 5.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 5, 12 or 3.
  6. 6.Two tanks hold 100 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  7. 7.Farhan takes 48 seconds and Diya 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?
  8. 8.Two tanks hold 175 litres and 125 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  9. 9.Two tanks hold 90 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  10. 10.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 6, 4 or 10.
  11. 11.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?
  12. 12.Diya takes 45 seconds and Arjun 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?
  13. 13.Two tanks hold 135 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.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?
  15. 15.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 4, 5 or 12.
  16. 16.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 8, 9 or 4.
  17. 17.Find the smallest number bigger than 15 that leaves a remainder of 5 when divided by 6, 15 or 12.
  18. 18.Meera takes 75 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?
  19. 19.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 5, 9 or 12.
  20. 20.Ishaan takes 45 seconds and Kabir 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?
  21. 21.Three temple bells ring every 30, 20 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Tara takes 45 seconds and Aarav 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?
  23. 23.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 6 or 3.
  24. 24.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 5, 6 or 15.
  25. 25.Three temple bells ring every 18, 6 and 30 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 12 that leaves a remainder of 3 when divided by 12, 4 or 6.
  27. 27.Two tanks hold 50 litres and 30 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, 10 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Saanvi takes 40 seconds and Aditya 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?
  30. 30.Two tanks hold 105 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  31. 31.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?
  32. 32.Three temple bells ring every 6, 5 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.Find the smallest number bigger than 12 that leaves a remainder of 4 when divided by 12, 9 or 5.
  34. 34.A hall floor is 360 cm long and 315 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  35. 35.Three temple bells ring every 18, 15 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.Two tanks hold 150 litres and 350 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  37. 37.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 3, 9 or 10.
  38. 38.Tara takes 30 seconds and Ishaan 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?
  39. 39.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?
  40. 40.Three temple bells ring every 10, 15 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 10
  2. 72
  3. 14
  4. 50
  5. 61
  6. 20
  7. 144
  8. 25
  9. 30
  10. 62
  11. 12
  12. 180
  13. 15
  14. 5
  15. 62
  16. 74
  17. 65
  18. 150
  19. 181
  20. 450
  21. 60
  22. 270
  23. 13
  24. 32
  25. 90
  26. 15
  27. 10
  28. 90
  29. 600
  30. 15
  31. 14
  32. 30
  33. 184
  34. 56
  35. 90
  36. 50
  37. 91
  38. 150
  39. 72
  40. 90

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