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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 262 · 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 8 that leaves a remainder of 2 when divided by 3, 8 or 6.
  2. 2.Three temple bells ring every 30, 24 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.Three temple bells ring every 10, 12 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  4. 4.Two tanks hold 40 litres and 35 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  5. 5.Dev takes 48 seconds and Nisha 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?
  6. 6.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 4, 9 or 5.
  7. 7.Three temple bells ring every 4, 9 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  8. 8.Two tanks hold 240 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  9. 9.A hall floor is 140 cm long and 80 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  10. 10.Aditya takes 60 seconds and Pooja takes 50 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 12, 10 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  12. 12.Karan takes 80 seconds and Arjun 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?
  13. 13.Three temple bells ring every 30, 4 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 4, 10 or 5.
  15. 15.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 4 or 8.
  16. 16.Ishaan takes 50 seconds and Farhan 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?
  17. 17.Pooja takes 48 seconds and Vivaan 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.Zoya takes 40 seconds and Kavya takes 50 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.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?
  20. 20.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?
  21. 21.Find the smallest number bigger than 5 that leaves a remainder of 1 when divided by 5, 4 or 3.
  22. 22.Three temple bells ring every 5, 18 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  23. 23.Three temple bells ring every 20, 15 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Three temple bells ring every 8, 5 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.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?
  26. 26.Kabir takes 36 seconds and Meera 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?
  27. 27.A hall floor is 480 cm long and 300 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  28. 28.Two tanks hold 75 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  29. 29.A hall floor is 400 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  30. 30.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?
  31. 31.Find the smallest number bigger than 6 that leaves a remainder of 1 when divided by 3, 4 or 6.
  32. 32.Three temple bells ring every 10, 12 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.Priya takes 72 seconds and Aarav 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?
  34. 34.Two tanks hold 150 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  35. 35.A hall floor is 150 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  36. 36.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?
  37. 37.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?
  38. 38.Three temple bells ring every 20, 24 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.Three temple bells ring every 8, 6 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  40. 40.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 5, 10 or 15.

Answer key

  1. 26
  2. 120
  3. 60
  4. 5
  5. 144
  6. 182
  7. 72
  8. 30
  9. 28
  10. 300
  11. 60
  12. 720
  13. 60
  14. 22
  15. 26
  16. 150
  17. 720
  18. 200
  19. 15
  20. 10
  21. 61
  22. 90
  23. 120
  24. 120
  25. 14
  26. 108
  27. 40
  28. 25
  29. 24
  30. 6
  31. 13
  32. 60
  33. 360
  34. 30
  35. 6
  36. 14
  37. 15
  38. 120
  39. 120
  40. 32

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