As far as I know the usual method for estimating the parameters in GMM is EM. However, it is also possible to use maximum likelihood. What are the differences between these two methods? Why would one prefer either of them?
You can use ML directly but as the priors of the different gaussians (usually called latent variables) are unknown, you'll probably find that your optimization objective is pretty hard. EM iterative method solves this intractability.
Suggested read: https://see.stanford.edu/materials/aimlcs229/cs229-notes8.pdf
Mehrin, you are in danger of creating a false dichotomy. EM is an optimisation technique that can be used to find maximum likelihood estimates and so the choice is not "one or the other".
In mixture models EM is often used to find MLEs or MAPs as it produces transparent algorithms.