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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 310 · 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).

NameDateTime takenScore ___ / 40
  1. 1.Sneha takes 36 seconds and Manav 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?
  2. 2.Two tanks hold 90 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  3. 3.Three temple bells ring every 5, 6 and 18 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 6 that leaves a remainder of 2 when divided by 4, 6 or 3.
  5. 5.A hall floor is 210 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  6. 6.Two tanks hold 60 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  7. 7.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 6, 10 or 9.
  8. 8.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?
  9. 9.Three temple bells ring every 12, 24 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.Three temple bells ring every 9, 15 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.Two tanks hold 400 litres and 350 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  12. 12.Two tanks hold 140 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.Three temple bells ring every 6, 9 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 10, 15 or 12.
  15. 15.Rohan takes 36 seconds and Zoya 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?
  16. 16.Aditya takes 54 seconds and Kabir 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?
  17. 17.Zoya takes 54 seconds and Priya 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?
  18. 18.Two tanks hold 125 litres and 150 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 60 litres and 75 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 100 litres and 225 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 4, 15 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 4, 3 or 8.
  23. 23.Two tanks hold 225 litres and 125 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  24. 24.A hall floor is 300 cm long and 240 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  25. 25.Two tanks hold 320 litres and 360 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 175 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  27. 27.Two tanks hold 15 litres and 25 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 4, 20 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Three temple bells ring every 6, 30 and 4 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 9 that leaves a remainder of 3 when divided by 4, 5 or 9.
  31. 31.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 4, 3 or 10.
  32. 32.Priya takes 45 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?
  33. 33.Two tanks hold 360 litres and 280 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  34. 34.Saanvi takes 40 seconds and Rohan 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?
  35. 35.Pooja takes 90 seconds and Isha 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?
  36. 36.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?
  37. 37.Kavya takes 40 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?
  38. 38.Two tanks hold 45 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  39. 39.Zoya takes 72 seconds and Aditya 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?
  40. 40.Two tanks hold 30 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?

Answer key

  1. 180
  2. 10
  3. 90
  4. 14
  5. 21
  6. 20
  7. 91
  8. 6
  9. 120
  10. 90
  11. 50
  12. 20
  13. 90
  14. 63
  15. 144
  16. 270
  17. 432
  18. 25
  19. 15
  20. 25
  21. 120
  22. 25
  23. 25
  24. 20
  25. 40
  26. 21
  27. 5
  28. 60
  29. 60
  30. 183
  31. 61
  32. 225
  33. 40
  34. 200
  35. 180
  36. 20
  37. 120
  38. 15
  39. 360
  40. 15

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