Lcm of Schur indices of irreducible representations

For a group over a field
Suppose $$G$$ is a group and $$K$$ is a field whose characteristic does not divide the order of $$G$$. The lcm of Schur indices of irreducible representations of $$G$$ over $$K$$ is defined as the least common multiple of all the Schur index values of all the irreducible linear representations of $$G$$ over $$K$$.

Typical context: finite group and splitting field
The typical context is where $$G$$ is a finite group and $$K$$ is a splitting field for $$G$$. In particular, the characteristic of $$K$$ is either zero or is a prime not dividing the order of $$G$$, and every irreducible representation of $$G$$ over any extension field of $$K$$ can be realized over $$K$$.