“Most Similar Vector Problem” on an Integer Lattice

Question

I am currently working on problem that I think could be expressed as an integer lattice problem, and hoping to find some guidance on this forum.

Given $u \in \mathbb{R}^n$ and a bounded integer lattice $L = \mathbb{Z}^n \cap [-M,M]^n$, I would like to find an integer vector $v \in L$ such that the angle between $u$ and $v$ is as small as possible. That is, I would like $$v \in \text{argmax}_{w \in L} \frac{u.w}{\|u\|\|w\|}$$

Here, the objective function is just the cosine between the vectors $u$ and $w$.

I am wondering if this problem can be formulated as a well-known integer lattice problem (such as a closest vector problem). If so, is there an algorithm that I could use to solve it? Any help or resources would be greatly appreciated.