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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 490 · 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.Three temple bells ring every 4, 15 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.Three temple bells ring every 4, 12 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.Find the smallest number bigger than 15 that leaves a remainder of 3 when divided by 5, 15 or 12.
  4. 4.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 12, 3 or 15.
  5. 5.Aditya takes 30 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?
  6. 6.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 3, 10 or 15.
  7. 7.Find the smallest number bigger than 5 that leaves a remainder of 2 when divided by 4, 5 or 3.
  8. 8.Three temple bells ring every 8, 9 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.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?
  10. 10.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 3, 9 or 10.
  11. 11.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 15, 10 or 5.
  12. 12.Two tanks hold 350 litres and 200 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  13. 13.Two tanks hold 450 litres and 400 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  14. 14.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?
  15. 15.A hall floor is 250 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  16. 16.Two tanks hold 20 litres and 30 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  17. 17.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 3, 9 or 15.
  18. 18.Three temple bells ring every 15, 8 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Rahul takes 36 seconds and Karan 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?
  20. 20.Two tanks hold 100 litres and 225 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  21. 21.A hall floor is 180 cm long and 150 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  22. 22.Isha takes 48 seconds and Rohan 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?
  23. 23.Three temple bells ring every 4, 8 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Three temple bells ring every 5, 8 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  25. 25.Three temple bells ring every 24, 5 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 5, 6 or 15.
  27. 27.Three temple bells ring every 20, 24 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  28. 28.Find the smallest number bigger than 15 that leaves a remainder of 9 when divided by 12, 10 or 15.
  29. 29.Kabir takes 40 seconds and Rohan 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?
  30. 30.Aditya takes 60 seconds and Diya 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?
  31. 31.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 15, 6 or 9.
  32. 32.Two tanks hold 35 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  33. 33.A hall floor is 210 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  34. 34.Three temple bells ring every 18, 4 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  35. 35.Rohan takes 90 seconds and Diya 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?
  36. 36.Arjun takes 40 seconds and Isha 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?
  37. 37.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?
  38. 38.Three temple bells ring every 20, 6 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  39. 39.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 4, 3 or 15.
  40. 40.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 4, 6 or 8.

Answer key

  1. 120
  2. 60
  3. 63
  4. 62
  5. 360
  6. 31
  7. 62
  8. 72
  9. 42
  10. 92
  11. 31
  12. 50
  13. 50
  14. 120
  15. 10
  16. 10
  17. 47
  18. 120
  19. 360
  20. 25
  21. 30
  22. 720
  23. 24
  24. 120
  25. 120
  26. 34
  27. 120
  28. 69
  29. 120
  30. 300
  31. 94
  32. 5
  33. 42
  34. 36
  35. 270
  36. 200
  37. 56
  38. 60
  39. 62
  40. 26

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