The least common multiple of positive integer d and 3-digit integer n is 690. If n is not divisible by 3 and d is not divisible by 2, what is the value of n? Choose the correct answer: A) 115 B) 230 C) 460 D) 575 E) 690

Rationale: the lcm of n and d is 690 = 2 * 3 * 5 * 23 . d is not divisible by 2 , thus 2 goes to n n is not divisible by 3 , thus 3 goes to d . 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 = 230 . answer : b .
Answer: B