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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 295 · 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.Farhan takes 72 seconds and Diya takes 90 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.A hall floor is 350 cm long and 300 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  3. 3.A hall floor is 240 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  4. 4.Three temple bells ring every 10, 4 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.Two tanks hold 20 litres and 15 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  6. 6.Two tanks hold 40 litres and 180 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 12 that leaves a remainder of 3 when divided by 4, 10 or 12.
  8. 8.Zoya takes 50 seconds and Arjun 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?
  9. 9.Two tanks hold 75 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  10. 10.Three temple bells ring every 30, 9 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.A hall floor is 200 cm long and 75 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  12. 12.A hall floor is 80 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  13. 13.Two tanks hold 180 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.Kavya takes 72 seconds and Rahul 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?
  15. 15.A hall floor is 270 cm long and 225 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  16. 16.Rahul takes 50 seconds and Nisha 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?
  17. 17.Three temple bells ring every 4, 9 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.A hall floor is 240 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  19. 19.Find the smallest number bigger than 8 that leaves a remainder of 3 when divided by 8, 5 or 6.
  20. 20.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?
  21. 21.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 5, 12 or 4.
  22. 22.Karan takes 40 seconds and Arjun 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?
  23. 23.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 3, 10 or 6.
  24. 24.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?
  25. 25.Ishaan takes 36 seconds and Rahul 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?
  26. 26.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 3, 5 or 6.
  27. 27.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 12, 6 or 5.
  28. 28.Three temple bells ring every 5, 6 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 3, 6 or 12.
  30. 30.Three temple bells ring every 20, 15 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.A hall floor is 125 cm long and 50 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 30, 20 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.A hall floor is 280 cm long and 160 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  34. 34.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?
  35. 35.Saanvi takes 90 seconds and Tara 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?
  36. 36.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?
  37. 37.Find the smallest number bigger than 12 that leaves a remainder of 5 when divided by 6, 8 or 12.
  38. 38.Two tanks hold 120 litres and 160 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  39. 39.Three temple bells ring every 4, 12 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  40. 40.Two tanks hold 80 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?

Answer key

  1. 360
  2. 42
  3. 24
  4. 60
  5. 5
  6. 20
  7. 63
  8. 150
  9. 15
  10. 90
  11. 24
  12. 12
  13. 30
  14. 360
  15. 30
  16. 300
  17. 36
  18. 12
  19. 123
  20. 40
  21. 61
  22. 360
  23. 32
  24. 21
  25. 720
  26. 31
  27. 63
  28. 60
  29. 13
  30. 120
  31. 10
  32. 60
  33. 28
  34. 40
  35. 270
  36. 30
  37. 29
  38. 40
  39. 24
  40. 40

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