abc ... not d?

Number Theory Level 4

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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