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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 292 · 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 120 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  2. 2.Farhan takes 60 seconds and Rahul 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?
  3. 3.Find the smallest number bigger than 12 that leaves a remainder of 4 when divided by 12, 8 or 10.
  4. 4.Nisha takes 50 seconds and Kabir 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?
  5. 5.Find the smallest number bigger than 12 that leaves a remainder of 4 when divided by 12, 5 or 9.
  6. 6.Diya takes 50 seconds and Saanvi 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?
  7. 7.A hall floor is 400 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  8. 8.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 6 or 4.
  9. 9.Dev takes 40 seconds and Nisha 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?
  10. 10.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 3, 5 or 10.
  11. 11.Three temple bells ring every 30, 4 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.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?
  13. 13.Arjun takes 90 seconds and Aarav 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?
  14. 14.Meera takes 45 seconds and Aarav 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?
  15. 15.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?
  16. 16.Three temple bells ring every 6, 4 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 3, 10 or 12.
  18. 18.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?
  19. 19.Two tanks hold 240 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  20. 20.Three temple bells ring every 24, 6 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.Three temple bells ring every 10, 8 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Three temple bells ring every 6, 20 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.Arjun takes 45 seconds and Dev 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?
  24. 24.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 12, 3 or 15.
  25. 25.Kavya takes 40 seconds and Manav 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?
  26. 26.Three temple bells ring every 24, 20 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.Three temple bells ring every 5, 10 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.A hall floor is 175 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  29. 29.Three temple bells ring every 15, 12 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 8 or 12.
  31. 31.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 4, 9 or 8.
  32. 32.Two tanks hold 175 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  33. 33.Diya takes 60 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?
  34. 34.Two tanks hold 135 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  35. 35.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 9, 5 or 15.
  36. 36.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?
  37. 37.Aarav takes 60 seconds and Pooja 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?
  38. 38.Farhan takes 36 seconds and Sneha 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?
  39. 39.A hall floor is 180 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  40. 40.Three temple bells ring every 24, 5 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 15
  2. 540
  3. 124
  4. 300
  5. 184
  6. 450
  7. 24
  8. 13
  9. 360
  10. 31
  11. 60
  12. 30
  13. 360
  14. 360
  15. 40
  16. 60
  17. 61
  18. 10
  19. 30
  20. 120
  21. 40
  22. 120
  23. 270
  24. 62
  25. 120
  26. 120
  27. 90
  28. 21
  29. 60
  30. 122
  31. 73
  32. 25
  33. 180
  34. 15
  35. 47
  36. 50
  37. 120
  38. 180
  39. 30
  40. 120

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