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Number Theory Level pending

The number \( \overline{987abc} \) is a multiple of 6, 7, 8 and 9. What is the value of \( \overline{abc} \)?

Details and assumptions

\( \overline{abc}\) means \( 100a + 10b + 1c\), as opposed to \( a \times b \times c\). As an explicit example, for \(a=2, b=3, c=4\), \(\overline{abc} = 234\) and not \( 2 \times 3 \times 4 = 24\).

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