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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 531 · 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.Find the smallest number bigger than 12 that leaves a remainder of 4 when divided by 5, 10 or 12.
  2. 2.Three temple bells ring every 30, 10 and 8 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 250 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  4. 4.Two tanks hold 90 litres and 240 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  5. 5.Two tanks hold 315 litres and 180 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  6. 6.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 9, 10 or 6.
  7. 7.Find the smallest number bigger than 15 that leaves a remainder of 6 when divided by 15, 12 or 10.
  8. 8.Three temple bells ring every 10, 15 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.A hall floor is 420 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  10. 10.A hall floor is 200 cm long and 175 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  11. 11.A hall floor is 480 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  12. 12.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 6, 5 or 15.
  13. 13.Aarav takes 54 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?
  14. 14.A hall floor is 100 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  15. 15.A hall floor is 240 cm long and 210 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  16. 16.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 3, 9 or 12.
  17. 17.Rahul takes 54 seconds and Zoya 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?
  18. 18.Three temple bells ring every 30, 6 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.A hall floor is 150 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  20. 20.Priya takes 54 seconds and Aditya 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?
  21. 21.Two tanks hold 160 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  22. 22.Find the smallest number bigger than 6 that leaves a remainder of 2 when divided by 3, 4 or 6.
  23. 23.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 3, 5 or 15.
  24. 24.Two tanks hold 180 litres and 405 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  25. 25.Two tanks hold 75 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  26. 26.Three temple bells ring every 20, 4 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 6, 5 or 10.
  28. 28.A hall floor is 175 cm long and 125 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  29. 29.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?
  30. 30.A hall floor is 100 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  31. 31.Three temple bells ring every 6, 20 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.Vivaan takes 50 seconds and Diya 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?
  33. 33.Ananya takes 40 seconds and Rohan 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?
  34. 34.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 10, 3 or 4.
  35. 35.Two tanks hold 75 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  36. 36.Two tanks hold 135 litres and 105 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  37. 37.A hall floor is 280 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  38. 38.Three temple bells ring every 10, 30 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.Priya takes 40 seconds and Meera 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?
  40. 40.Three temple bells ring every 5, 30 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 64
  2. 120
  3. 35
  4. 30
  5. 45
  6. 92
  7. 66
  8. 30
  9. 14
  10. 56
  11. 24
  12. 31
  13. 270
  14. 20
  15. 56
  16. 37
  17. 270
  18. 60
  19. 10
  20. 216
  21. 20
  22. 14
  23. 17
  24. 45
  25. 15
  26. 60
  27. 31
  28. 35
  29. 10
  30. 10
  31. 60
  32. 150
  33. 600
  34. 62
  35. 15
  36. 15
  37. 35
  38. 120
  39. 360
  40. 120

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