Are you familiar with abundant numbers?

An abundant number is a number whose factors (excluding itself) sum to a number greater than itself. $1 \Rightarrow 0 = 0$

$2 \Rightarrow 1 = 1$

$3 \Rightarrow 1 = 1$

$4 \Rightarrow 1+2 = 3$

$5 \Rightarrow 1 = 1$

$6 \Rightarrow 1+2+3 = 6$ 6 is a perfect number, whose factors sum to itself! Sadly, not what we want.

$7 \Rightarrow 1 = 1$

$8 \Rightarrow 1+2+4 = 7$

$9 \Rightarrow 1+3 = 4$

$10 \Rightarrow 1+2+5 = 8$

$11 \Rightarrow 1 = 1$

$12 \Rightarrow 1+2+3+4+6 = 16$ ! $16>12$ $\boxed{12}$ is the first to work and the answer.