The least common multiple of positive integer m and 3digit integer n is 690. If n is not divisible by 3 and m is not divisible by 2, what is the value of n? A. 115 B. 230 C. 460 D. 575 E. 690
(B) We factorize 690 = 2 × 3 × 115 = 2 × 3 × 5 × 23. Dividing 690 starting by the smallest factor we get possible values for 3digit integer n: 690, 690 / 2 = 345, 690 / 3 = 230, 690 / 5 = 138, 690 / 6 = 115. 690 / 10 = 69 which is a 2digit number, therefore n must be one of the following: 690, 345, 230, 138, 115.
n is not divisible by 3. So we eliminate 690, 345, 138. m is not divisible by 2, but the least common multiple of m and n is. So n must be divisible by 2. We eliminate 115. That leaves us only one option for n, 230. The answer is (B).  Hi, I understand why 690, 345, 138 are eliminated. But I do not understand why 115 was eliminated. Since this number is not divisible by 2 or 3. Where as 230 is divisible by 2 but not by 3.
