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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 104 · 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 200 cm long and 125 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  2. 2.Karan takes 72 seconds and Kabir 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?
  3. 3.Ananya takes 30 seconds and Tara 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?
  4. 4.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?
  5. 5.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 8 or 9.
  6. 6.Three temple bells ring every 15, 4 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.Two tanks hold 150 litres and 350 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  8. 8.Find the smallest number bigger than 12 that leaves a remainder of 3 when divided by 12, 6 or 4.
  9. 9.Three temple bells ring every 30, 12 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  10. 10.Aarav takes 48 seconds and Zoya 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?
  11. 11.Three temple bells ring every 5, 24 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.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?
  13. 13.Three temple bells ring every 4, 10 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.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?
  15. 15.Find the smallest number bigger than 9 that leaves a remainder of 3 when divided by 5, 9 or 4.
  16. 16.Three temple bells ring every 6, 10 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  17. 17.Three temple bells ring every 15, 9 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.Ishaan takes 72 seconds and Rohan 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?
  19. 19.Vivaan takes 48 seconds and Sneha 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?
  20. 20.Pooja takes 75 seconds and Priya 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?
  21. 21.Find the smallest number bigger than 15 that leaves a remainder of 7 when divided by 8, 12 or 15.
  22. 22.Three temple bells ring every 8, 15 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 5, 8 or 3.
  24. 24.A hall floor is 175 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  25. 25.Two tanks hold 160 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  26. 26.Two tanks hold 175 litres and 150 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  27. 27.Three temple bells ring every 10, 9 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.Three temple bells ring every 6, 20 and 24 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 15 that leaves a remainder of 2 when divided by 3, 15 or 9.
  30. 30.Two tanks hold 120 litres and 280 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  31. 31.Three temple bells ring every 9, 18 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.Three temple bells ring every 12, 15 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 10, 6 or 5.
  34. 34.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 9, 3 or 5.
  35. 35.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 3, 8 or 5.
  36. 36.Two tanks hold 60 litres and 210 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 15 that leaves a remainder of 1 when divided by 4, 12 or 15.
  38. 38.Three temple bells ring every 10, 6 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, 30 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  40. 40.Dev takes 72 seconds and Nisha 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?

Answer key

  1. 40
  2. 216
  3. 150
  4. 15
  5. 74
  6. 120
  7. 50
  8. 15
  9. 60
  10. 240
  11. 120
  12. 15
  13. 60
  14. 35
  15. 183
  16. 30
  17. 90
  18. 360
  19. 144
  20. 300
  21. 127
  22. 120
  23. 121
  24. 42
  25. 20
  26. 25
  27. 90
  28. 120
  29. 47
  30. 40
  31. 90
  32. 120
  33. 33
  34. 46
  35. 122
  36. 30
  37. 61
  38. 90
  39. 90
  40. 360

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