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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 242 · 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 5 that leaves a remainder of 2 when divided by 4, 3 or 5.
  2. 2.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 9, 12 or 4.
  3. 3.Dev takes 36 seconds and Diya 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?
  4. 4.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 3, 9 or 6.
  5. 5.Three temple bells ring every 15, 8 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  6. 6.Three temple bells ring every 24, 15 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  7. 7.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 6, 10 or 4.
  8. 8.Manav takes 90 seconds and Kavya 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?
  9. 9.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?
  10. 10.Three temple bells ring every 4, 24 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  11. 11.Sneha takes 30 seconds and Kavya 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?
  12. 12.Three temple bells ring every 5, 6 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  13. 13.Find the smallest number bigger than 9 that leaves a remainder of 1 when divided by 4, 6 or 9.
  14. 14.Two tanks hold 45 litres and 75 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  15. 15.Three temple bells ring every 8, 6 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 15, 4 or 12.
  17. 17.Three temple bells ring every 6, 8 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.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?
  19. 19.A hall floor is 480 cm long and 420 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  20. 20.Aditya takes 30 seconds and Pooja 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?
  21. 21.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 9, 12 or 5.
  22. 22.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 3 or 9.
  23. 23.A hall floor is 360 cm long and 135 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  24. 24.Rohan takes 80 seconds and Kabir 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?
  25. 25.A hall floor is 360 cm long and 300 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  26. 26.A hall floor is 150 cm long and 60 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  27. 27.Farhan takes 60 seconds and Karan takes 48 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?
  28. 28.Find the smallest number bigger than 10 that leaves a remainder of 4 when divided by 5, 10 or 6.
  29. 29.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?
  30. 30.Arjun takes 36 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?
  31. 31.A hall floor is 175 cm long and 125 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  32. 32.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 10, 3 or 4.
  33. 33.Three temple bells ring every 9, 15 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.Three temple bells ring every 12, 30 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.Two tanks hold 120 litres and 45 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  36. 36.Pooja takes 60 seconds and Isha 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?
  37. 37.A hall floor is 125 cm long and 50 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  38. 38.Ishaan takes 45 seconds and Saanvi 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?
  39. 39.A hall floor is 100 cm long and 80 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 6 that leaves a remainder of 2 when divided by 3, 6 or 5.

Answer key

  1. 62
  2. 37
  3. 180
  4. 20
  5. 120
  6. 120
  7. 62
  8. 720
  9. 10
  10. 120
  11. 120
  12. 120
  13. 37
  14. 15
  15. 120
  16. 62
  17. 24
  18. 35
  19. 56
  20. 150
  21. 182
  22. 46
  23. 24
  24. 720
  25. 30
  26. 10
  27. 240
  28. 34
  29. 42
  30. 360
  31. 35
  32. 62
  33. 45
  34. 60
  35. 15
  36. 180
  37. 10
  38. 450
  39. 20
  40. 32

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