# Can LDA assign more than one topic for a word?

I have just started reading about Latent Dirichlet Allocation LDA and want to apply it to my project.

May I know if LDA is able to assign a topic to more than one word?

For example, Article A talks about "river banks" while Article B talks about "The role of banks in finance". Hence, will LDA allow the word "banks" to potentially be assigned to two different topics?

The result of any LDA inference algorithm is $\theta_{d,t}$ and $\phi_{t,w}$, distribution of topics in each document and distribution of terms in each topics. Given these distributions, one can obtain estimate for $p(z|d,w)$, conditional probability of a topic $z$ for word $w$ in document $d$: $$p(z|d,w)=\frac{p(z,d,w)}{\sum\limits_{s=1}^K p(s,d,w)}=\frac{\theta_{d,z} \phi_{z,w}}{\sum\limits_{s=1}^{K} \theta_{d, s} \phi_{s, w}}$$ Further utilizing of this information can be, for example, assigning the single most probable topic for a word. But it's not obligatory.