I am only given one signal, $x(t)=\cos (200t)$, and I need to determine its fundamental angular frequency. But I'm a bit confused by the concept.
I only have 1 signal, but from Google I know that the fundamental frequency is the lcm of two signal's frequencies.
You appear to have picked up a couple of misunderstandings from your Google searches. The fundamental frequency of a periodic function is merely the inverse of its fundamental period (i.e. its shortest period). It's the gcd (and normally the lowest) of the frequencies of the sinusoids appearing in the function's Fourier expansion. The frequencies of all those sinusoids will be integral multiples of the fundamental frequency.
The fundamental frequency of the sum of just two sinusoids, the ratio of whose frequencies is a rational number, is the gcd (not the lcm) of their frequencies.
The fundamental frequency of a pure sinusoid (i.e. $\ \cos(at+b)\ $ or $\ \sin(at+b)\ $) is thus just its freqency, $\ \frac{a}{2\pi}\ $. I've never heard the term "fundamental" applied to angular frequencies, but I would presume that "fundamental angular frequency" simply means $\ 2\pi\ $ times the fundamental frequency, in which case your answer of $200$ radians per unit time would be correct for the function $\ \cos(200t)\ $.