  By considering the closure property of a Lagrangian multiform as a
conservation law, we use Noether's theorem to show that every variational
symmetry of a Lagrangian leads to a Lagrangian multiform. In doing so, we
provide a systematic method for constructing Lagrangian multiforms for which
the closure property and the multiform Euler-Lagrange (EL) equations both hold.
We present three examples, including the first known example of a Lagrangian
3-form: a multiform for the Kadomtsev-Petviashvili equation. We also present a
new proof of the multiform EL equations for a Lagrangian k-form for arbitrary
k.
