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We compute the integral Picard group of the stack $\mathcal{M}_{2l}$ ofpolarized K3 surfaces with at most rational double points of degree $2l=4,6,8$.We show that in this range the integral Picard group is torsion-free and that abasis is given by certain elliptic Noether-Lefschetz divisors together with theHodge line bundle. To achieve this result, we investigate certain stacks ofcomplete intersections and their Picard groups by means of equivariantgeometry. In the end we compute an expression of the class of someNoether-Lefschetz divisors, restricted to an open substack of$\mathcal{M}_{2l}$, in terms of the basis mentioned above.

Integral Picard group of some stacks of polarized K3 surfaces of low degree