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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 566 · 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.A hall floor is 280 cm long and 240 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  2. 2.Rahul takes 36 seconds and Farhan 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?
  3. 3.Two tanks hold 50 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  4. 4.A hall floor is 280 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  5. 5.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?
  6. 6.Two tanks hold 210 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.A hall floor is 175 cm long and 50 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 15 that leaves a remainder of 2 when divided by 3, 15 or 9.
  9. 9.Three temple bells ring every 18, 6 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.Three temple bells ring every 30, 4 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.Three temple bells ring every 4, 20 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.Three temple bells ring every 10, 4 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.Two tanks hold 280 litres and 240 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.Three temple bells ring every 24, 10 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  15. 15.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?
  16. 16.Sneha takes 75 seconds and Ananya 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.A hall floor is 250 cm long and 200 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  18. 18.Nisha takes 80 seconds and Vivaan 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 8 that leaves a remainder of 2 when divided by 6, 3 or 8.
  20. 20.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 6, 5 or 10.
  21. 21.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 10, 15 or 8.
  22. 22.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 4, 3 or 8.
  23. 23.A hall floor is 350 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  24. 24.Two tanks hold 200 litres and 320 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  25. 25.Three temple bells ring every 30, 4 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 9, 4 or 12.
  27. 27.Two tanks hold 150 litres and 210 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 8, 24 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Sneha takes 54 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?
  30. 30.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 12, 8 or 5.
  31. 31.Two tanks hold 100 litres and 250 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  32. 32.Three temple bells ring every 6, 9 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.Find the smallest number bigger than 10 that leaves a remainder of 3 when divided by 4, 9 or 10.
  34. 34.Three temple bells ring every 24, 4 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.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?
  36. 36.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 8 or 4.
  37. 37.Aarav takes 48 seconds and Kavya 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?
  38. 38.Karan takes 40 seconds and Aarav 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?
  39. 39.A hall floor is 400 cm long and 250 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  40. 40.Find the smallest number bigger than 10 that leaves a remainder of 4 when divided by 10, 8 or 6.

Answer key

  1. 42
  2. 180
  3. 10
  4. 14
  5. 40
  6. 30
  7. 14
  8. 47
  9. 90
  10. 60
  11. 60
  12. 60
  13. 40
  14. 120
  15. 21
  16. 300
  17. 20
  18. 720
  19. 26
  20. 32
  21. 122
  22. 25
  23. 21
  24. 40
  25. 60
  26. 37
  27. 30
  28. 120
  29. 270
  30. 123
  31. 50
  32. 72
  33. 183
  34. 120
  35. 10
  36. 26
  37. 432
  38. 120
  39. 40
  40. 124

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