Countdown

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 $2 \times 3 \times 4 = 24$ .