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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 404 · 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 15 that leaves a remainder of 1 when divided by 5, 12 or 15.
  2. 2.Three temple bells ring every 18, 5 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  3. 3.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?
  4. 4.Diya takes 40 seconds and Meera 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?
  5. 5.Three temple bells ring every 5, 6 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 6, 10 and 18 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 1 when divided by 10, 6 or 3.
  8. 8.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 5, 3 or 8.
  9. 9.Rohan takes 60 seconds and Manav 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?
  10. 10.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?
  11. 11.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 3, 12 or 10.
  12. 12.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 3, 6 or 15.
  13. 13.Find the smallest number bigger than 15 that leaves a remainder of 2 when divided by 12, 15 or 4.
  14. 14.Two tanks hold 125 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 20, 24 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  16. 16.Three temple bells ring every 5, 9 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 5, 20 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.Three temple bells ring every 20, 12 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.Three temple bells ring every 6, 12 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  20. 20.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 4, 12 or 3.
  21. 21.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 6, 4 or 8.
  22. 22.A hall floor is 400 cm long and 350 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  23. 23.Three temple bells ring every 30, 12 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.Find the smallest number bigger than 9 that leaves a remainder of 3 when divided by 6, 4 or 9.
  25. 25.Three temple bells ring every 20, 8 and 15 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  26. 26.Two tanks hold 45 litres and 60 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  27. 27.Find the smallest number bigger than 15 that leaves a remainder of 1 when divided by 6, 15 or 3.
  28. 28.Two tanks hold 15 litres and 25 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  29. 29.Two tanks hold 405 litres and 315 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  30. 30.A hall floor is 360 cm long and 315 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  31. 31.Two tanks hold 360 litres and 160 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  32. 32.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?
  33. 33.Three temple bells ring every 12, 9 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  34. 34.A hall floor is 200 cm long and 160 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  35. 35.Two tanks hold 90 litres and 105 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  36. 36.Three temple bells ring every 15, 5 and 24 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  37. 37.Kavya takes 72 seconds and Meera 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?
  38. 38.Three temple bells ring every 24, 30 and 6 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 5 that leaves a remainder of 1 when divided by 3, 5 or 4.
  40. 40.Kavya takes 72 seconds and Isha 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?

Answer key

  1. 61
  2. 90
  3. 6
  4. 360
  5. 60
  6. 90
  7. 31
  8. 122
  9. 300
  10. 90
  11. 61
  12. 32
  13. 62
  14. 25
  15. 120
  16. 45
  17. 60
  18. 60
  19. 60
  20. 13
  21. 26
  22. 56
  23. 120
  24. 39
  25. 120
  26. 15
  27. 31
  28. 5
  29. 45
  30. 56
  31. 40
  32. 36
  33. 36
  34. 20
  35. 15
  36. 120
  37. 360
  38. 120
  39. 61
  40. 360

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