What A Way To Factorize It!

Number Theory Level 1

\[ \large 2000 \mid a^b \times b^a \]

Let \(a\) and \(b\) be two positive integers such that \({ a }^{ b }\times { b }^{ a }\) is divisible by \(2000\). Find the least value of the product of \(a\) and \(b\).