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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 68 · 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 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  2. 2.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?
  3. 3.Two tanks hold 125 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  4. 4.Three temple bells ring every 20, 12 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.Two tanks hold 25 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.Aarav takes 72 seconds and Manav 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?
  7. 7.A hall floor is 135 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  8. 8.Three temple bells ring every 5, 9 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.Three temple bells ring every 8, 18 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.Three temple bells ring every 20, 12 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.Find the smallest number bigger than 15 that leaves a remainder of 5 when divided by 15, 10 or 9.
  12. 12.A hall floor is 315 cm long and 225 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  13. 13.Aarav takes 60 seconds and Rahul 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?
  14. 14.A hall floor is 200 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  15. 15.A hall floor is 150 cm long and 90 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 8 that leaves a remainder of 2 when divided by 8, 4 or 3.
  17. 17.Vivaan takes 60 seconds and Priya 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?
  18. 18.Kavya takes 40 seconds and Ishaan 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?
  19. 19.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 6, 5 or 15.
  20. 20.Arjun takes 54 seconds and Rahul 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.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 8, 6 or 9.
  22. 22.A hall floor is 250 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  23. 23.Two tanks hold 240 litres and 270 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  24. 24.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?
  25. 25.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 8, 15 or 5.
  26. 26.Two tanks hold 45 litres and 40 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  27. 27.A hall floor is 320 cm long and 280 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  28. 28.Three temple bells ring every 18, 10 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Two tanks hold 75 litres and 125 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  30. 30.Three temple bells ring every 8, 9 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  31. 31.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 8, 12 or 15.
  32. 32.Three temple bells ring every 4, 15 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.A hall floor is 140 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  34. 34.Pooja takes 75 seconds and Manav 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?
  35. 35.Three temple bells ring every 15, 30 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 4, 15 or 6.
  37. 37.Three temple bells ring every 10, 30 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.Three temple bells ring every 30, 5 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.Three temple bells ring every 9, 6 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  40. 40.Three temple bells ring every 6, 10 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?

Answer key

  1. 21
  2. 56
  3. 25
  4. 120
  5. 5
  6. 216
  7. 6
  8. 90
  9. 72
  10. 60
  11. 95
  12. 35
  13. 180
  14. 15
  15. 15
  16. 26
  17. 240
  18. 600
  19. 34
  20. 216
  21. 74
  22. 15
  23. 30
  24. 15
  25. 121
  26. 5
  27. 56
  28. 90
  29. 25
  30. 72
  31. 122
  32. 60
  33. 42
  34. 600
  35. 60
  36. 62
  37. 120
  38. 90
  39. 72
  40. 60

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