If n is the smallest integer such that 72 times n is the square of an integer, what is the value of n?  Choose the most appropriate option: A) 2 B) 3 C) 6 D) 12 E) 24
72 can written as = 2 * 2 * 2 * 3 * 3 --&gt; 2^3 * 3^2---(1)   so for 72 * n to be a square of an integer, the integer should have even powers to the prime numbers it composed of.   here 2 already has even power -&gt; So n has to be 3 to make the power of 2 in (1) even   Option 2 is correct
<result>A</result>
If n is the smallest integer such that 72 times n is the square of an integer, what is the value of n?