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Answer:

The largest three-digit number divisible by 24 and 54 is:

  • 864

Step-by-step explanation:

To identify the largest number what I did was dividing 999 (the largest whole three-digit number of all) in the first number given (24):

  • [tex]\frac{999}{24}=41.625[/tex]

With this number, you know that you must multiply 24 by a number like 41 or less until you find a number that can be divisible by 54 and obtain a whole number, so:

  • 24*41= 984/54= 18.22 (how the number obtained is not a whole number, this is not the correct).
  • 24*40= 960/54= 17.77 (this is not).
  • 24*39= 936/54= 17.33 (this is not).
  • 24*38= 912/54= 16.88 (this is not).
  • 24*37=888/54= 16.44 (this is not).
  • 24*36= 864/54= 16 (This is the correct).

Now, you have identified that the number 864, you can prove it by dividing this in 24 and 54:

  • [tex]\frac{864}{24}=36[/tex]
  • [tex]\frac{864}{54}= 16[/tex]

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