# abc ... not d?

a,b and c are single digit natural numbers. If

$$\overline { aaaaaa }=b\times c\times \overline { bc } \times (2c-b)\times (2b+c)$$
Find $$a\times b\times c$$.

Details and Assumption $$\overline { xyz }$$ is a three digit number of the form $$100x+10y+z$$

This problem is a part of my set The Best of Me

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