let's take a peek at the denominators first off, and do a "prime factoring" on them.
25 = 5 * 5
27 = 3 * 3 * 3
45 = 3 * 3 * 5
the numbers in bold are repeated there more than once among the factors, and therefore we'll use them once, so our LCD will be 5 * 5 * 3 * 3 * 3, or 675.
[tex]\bf \stackrel{Alaska}{\cfrac{4}{25}}~+~\stackrel{Texas}{\cfrac{2}{27}}~+~\stackrel{California}{\cfrac{2}{45}}~~ \stackrel{LCD~675}{\implies }~~ \cfrac{(27)4~+~(25)2~+~(15)2}{675}
\\\\\\
\cfrac{108+50+30}{675}\implies \cfrac{188}{675}[/tex]
