The least common multiple of positive integer q and 3-digit integer n is 690. If n is not divisible by 3 and q is not divisible by 2, what is the value of n?  Choose the correct choice from the following options.
A) 115
B) 230
C) 460
D) 575
E) 690
The LCM of n and q is 690 = 2*3*5*23.   q is not divisible by 2, thus 2 goes to n   n is not divisible by 3, thus 3 goes to q.   From above:   n must be divisible by 2 and not divisible by 3: n = 2*... In order n to be a 3-digit number it must take all other primes too: n = 2*5*23= 
<gadget id="calculator">2*5*23</gadget>
<output>230</output>
230.   Answer: 230.
<result>B</result>
The least common multiple of positive integer q and 3-digit integer n is 690. If n is not divisible by 3 and q is not divisible by 2, what is the value of n?