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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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