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Continuing the work of \cite{7} and \cite{8}, we derive an analogue of theclassical "$k/12$-formula" for Drinfeld modular forms of rank $r \geq 2$. Herethe vanishing order $\nu_{\omega}(f)$ of one modular form at some point$\omega$ of the complex upper half-plane is replaced by the intersectionmultiplicity $\nu_{\bo}(f_1,\ldots,f_{r-1})$ of $r-1$ independent Drinfeldmodular forms at some point $\bo$ of the Drinfeld symmetric space $\OM^r$. Weapply the formula to determine the common zeroes of $r-1$ consecutiveEisenstein series $E_{q^{i}-1}$, where $n-r<i<n$ for some $n \geq r$.

On Drinfeld modular forms of higher rank III: The analogue of the k/12-formula