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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 476 · 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.Three temple bells ring every 20, 30 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.A hall floor is 210 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  3. 3.Ananya takes 90 seconds and Isha 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?
  4. 4.Find the smallest number bigger than 10 that leaves a remainder of 5 when divided by 10, 9 or 6.
  5. 5.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 10, 3 or 12.
  6. 6.Diya takes 48 seconds and Dev 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?
  7. 7.Two tanks hold 100 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  8. 8.Three temple bells ring every 12, 4 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.Two tanks hold 240 litres and 210 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 15 that leaves a remainder of 3 when divided by 10, 8 or 15.
  11. 11.Find the smallest number bigger than 6 that leaves a remainder of 2 when divided by 5, 6 or 4.
  12. 12.A hall floor is 240 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  13. 13.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?
  14. 14.A hall floor is 315 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  15. 15.A hall floor is 360 cm long and 135 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 18, 15 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.A hall floor is 150 cm long and 125 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  18. 18.Diya takes 60 seconds and Sneha 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 10 that leaves a remainder of 2 when divided by 10, 4 or 6.
  20. 20.Three temple bells ring every 20, 12 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  21. 21.A hall floor is 120 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  22. 22.Rohan takes 45 seconds and Kavya 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?
  23. 23.Two tanks hold 35 litres and 10 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  24. 24.Find the smallest number bigger than 12 that leaves a remainder of 6 when divided by 9, 10 or 12.
  25. 25.Rahul takes 75 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?
  26. 26.Three temple bells ring every 9, 10 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.Three temple bells ring every 10, 8 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.Two tanks hold 40 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  29. 29.A hall floor is 300 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  30. 30.Farhan takes 45 seconds and Arjun 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?
  31. 31.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 4, 6 or 8.
  32. 32.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?
  33. 33.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 12, 9 or 6.
  34. 34.Three temple bells ring every 24, 4 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.Find the smallest number bigger than 9 that leaves a remainder of 3 when divided by 6, 9 or 4.
  36. 36.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?
  37. 37.Priya takes 75 seconds and Dev 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.Farhan takes 36 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?
  39. 39.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?
  40. 40.Two tanks hold 60 litres and 140 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?

Answer key

  1. 60
  2. 42
  3. 360
  4. 95
  5. 62
  6. 240
  7. 25
  8. 60
  9. 30
  10. 123
  11. 62
  12. 30
  13. 12
  14. 28
  15. 24
  16. 90
  17. 30
  18. 180
  19. 62
  20. 60
  21. 6
  22. 720
  23. 5
  24. 186
  25. 600
  26. 90
  27. 40
  28. 10
  29. 15
  30. 720
  31. 26
  32. 10
  33. 37
  34. 120
  35. 39
  36. 21
  37. 300
  38. 108
  39. 20
  40. 20

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