【Analysis】 676
Assume the largest number is $x$; if the direction of the “ $L$ ”-shaped frame is such that $x-8+x-7+x=2015$, then $x$ has no solution; if the direction of the “ $L$ ”-shaped frame is such that $x-7+x-6+x=2015$, then solving for $x$ gives $x=676$; if the direction of the “ $L$ ”-shaped frame is such that $x-7+x-1+x=2015$, then $x$ has no solution; if the direction of the “ $L$ ”-shaped frame is such that $x-8+x-1+x=2015$, then $x$ has no solution; in summary, the largest number is 676.
11. As shown in the figure, positive integers starting from 1 are arranged in the following form, and a "L" shaped pattern composed of 3 squares (which can be rotated) is used to frame three of these numbers (in the figure, the sum of the three numbers framed is $10+11+18=39$). If the sum of the three numbers framed by such a "L" shape is 2015, then the largest number among them is $\qquad$.