By definition of multiples of a number, the smallest possible integer value of n for which 99n is a multiple of 24 is n=8.
The multiples of a number are all the possible results of multiplying that number by each and every one of the natural numbers. In other words, a number is a multiple of another if it contains it an integer number of times.
The set of multiples of a given number (except zero) is infinite, since there are natural infinities to multiply.
You want to know the smallest possible integer value of n for which 99n is a multiple of 24.
Then, being x a natural number by which you multiply 24, this can be expressed as:
99n= 24x
Solving:
[tex]\frac{n}{x} =\frac{24}{99}[/tex]
Dividing both numbers by 3:
[tex]\frac{n}{x} =\frac{8}{3}[/tex]
Then:
Finally, the smallest possible integer value of n for which 99n is a multiple of 24 is n=8.
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