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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 487 · 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 12, 10 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  2. 2.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?
  3. 3.A hall floor is 480 cm long and 180 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  4. 4.Find the smallest number bigger than 15 that leaves a remainder of 5 when divided by 15, 8 or 6.
  5. 5.A hall floor is 320 cm long and 280 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  6. 6.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?
  7. 7.Two tanks hold 90 litres and 20 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 120 cm long and 100 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  9. 9.Find the smallest number bigger than 15 that leaves a remainder of 4 when divided by 10, 15 or 5.
  10. 10.Kavya takes 72 seconds and Ananya 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?
  11. 11.Find the smallest number bigger than 10 that leaves a remainder of 2 when divided by 10, 9 or 6.
  12. 12.Three temple bells ring every 8, 15 and 6 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 15 that leaves a remainder of 1 when divided by 4, 15 or 3.
  14. 14.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 5, 8 or 12.
  15. 15.Find the smallest number bigger than 9 that leaves a remainder of 5 when divided by 6, 8 or 9.
  16. 16.Three temple bells ring every 4, 30 and 8 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, 18 and 9 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  18. 18.Three temple bells ring every 10, 24 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  19. 19.A hall floor is 160 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 200 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  21. 21.Three temple bells ring every 20, 12 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  22. 22.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 6, 4 or 12.
  23. 23.Three temple bells ring every 15, 24 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  24. 24.A hall floor is 140 cm long and 40 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  25. 25.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?
  26. 26.Three temple bells ring every 15, 5 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  27. 27.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 10, 8 or 3.
  28. 28.Three temple bells ring every 18, 10 and 5 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  29. 29.Three temple bells ring every 20, 12 and 6 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.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?
  31. 31.Three temple bells ring every 10, 12 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.Three temple bells ring every 24, 30 and 20 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  33. 33.Two tanks hold 60 litres and 135 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  34. 34.Two tanks hold 250 litres and 450 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 5, 20 and 30 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  36. 36.Two tanks hold 150 litres and 100 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  37. 37.Three temple bells ring every 6, 20 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  38. 38.Three temple bells ring every 30, 6 and 8 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 1 when divided by 15, 3 or 5.
  40. 40.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 12, 3 or 10.

Answer key

  1. 60
  2. 30
  3. 24
  4. 125
  5. 56
  6. 56
  7. 10
  8. 30
  9. 34
  10. 360
  11. 92
  12. 120
  13. 61
  14. 122
  15. 77
  16. 120
  17. 90
  18. 120
  19. 24
  20. 15
  21. 60
  22. 13
  23. 120
  24. 14
  25. 90
  26. 60
  27. 121
  28. 90
  29. 60
  30. 30
  31. 60
  32. 120
  33. 15
  34. 50
  35. 60
  36. 50
  37. 60
  38. 120
  39. 16
  40. 62

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