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

If natural numbers $a,b,c$ satisfy the above equation , find the product $abc$ .

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Details And Assumptions:
**

- $\overline{bc}$ is a two digit number and $\overline{aaaaaa}$ is a six digit number.

The answer is 84.

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we can write the LHS as 111111a, 111111a = 3×7×11×13×37×a then we put b = 3 and c = 7. Finally we got a = 4. So, abc = 4.3.7 = 84