The smallest possible integer value of n for which 99n is a multiple of 24

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.

Value of n

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:

\(\frac{n}{x} =\frac{24}{99}\)

Dividing both numbers by 3:

\(\frac{n}{x} =\frac{8}{3}\)

Then:

n= 8
x= 3

Finally, the smallest possible integer value of n for which 99n is a multiple of 24 is n=8.

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