It's not correct.
According to the Cambridge Grammar of the English Language, single-syllable adjectives typically take "-er" and "-est" forms (eg "small → smaller → smallest") while multi-syllable adjectives typically use "more" and "most" (eg., "beautiful → more beautiful → most beautiful"). There are of course exceptions to this ("fun" springs to mind) but words tend to be used one way or the other, and "cheapest" is the idiomatic choice.