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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 501 · 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.Aditya takes 36 seconds and Karan 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?
  2. 2.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 10, 5 or 6.
  3. 3.A hall floor is 120 cm long and 90 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  4. 4.Three temple bells ring every 6, 24 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  5. 5.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 8, 6 or 12.
  6. 6.Three temple bells ring every 5, 18 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.Two tanks hold 10 litres and 35 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  8. 8.A hall floor is 150 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  9. 9.Meera takes 90 seconds and Vivaan 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?
  10. 10.Two tanks hold 50 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  11. 11.A hall floor is 300 cm long and 120 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 12 that leaves a remainder of 1 when divided by 3, 12 or 9.
  13. 13.Two tanks hold 450 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.Aarav takes 30 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?
  15. 15.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?
  16. 16.Sneha takes 40 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?
  17. 17.Three temple bells ring every 4, 18 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.Three temple bells ring every 5, 30 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Two tanks hold 105 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  20. 20.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?
  21. 21.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 4, 10 or 9.
  22. 22.Three temple bells ring every 6, 8 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.Diya takes 40 seconds and Isha 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?
  24. 24.Two tanks hold 20 litres and 90 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 6 that leaves a remainder of 3 when divided by 4, 5 or 6.
  26. 26.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 3, 6 or 8.
  27. 27.Three temple bells ring every 18, 6 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.Zoya takes 72 seconds and Diya 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?
  29. 29.Two tanks hold 10 litres and 15 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  30. 30.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 10, 5 or 3.
  31. 31.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 9, 15 or 3.
  32. 32.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 4, 6 or 8.
  33. 33.Three temple bells ring every 15, 10 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.Two tanks hold 180 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  35. 35.Three temple bells ring every 20, 10 and 6 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 6 when divided by 8, 10 or 15.
  37. 37.Three temple bells ring every 12, 10 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.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?
  39. 39.Three temple bells ring every 10, 6 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  40. 40.A hall floor is 100 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?

Answer key

  1. 108
  2. 32
  3. 12
  4. 120
  5. 25
  6. 90
  7. 5
  8. 20
  9. 180
  10. 10
  11. 10
  12. 37
  13. 50
  14. 150
  15. 90
  16. 360
  17. 36
  18. 60
  19. 15
  20. 72
  21. 181
  22. 120
  23. 360
  24. 10
  25. 63
  26. 26
  27. 90
  28. 360
  29. 5
  30. 32
  31. 47
  32. 26
  33. 30
  34. 45
  35. 60
  36. 126
  37. 60
  38. 30
  39. 60
  40. 15

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