LU growth factor applied to LDL of a Positive Semidefinite matrix [closed]

Question

For a Positive Semidefinite matrix $A$, which we can decompose through $LDL$ decomposition as follows: $A=LDL^\text{T}$; how can we prove that for a decomposition $A=LU=L(DL^\text{T})$, the growth factor $g$ is less than or equal to 1?