Does every mantra begin with/contain ॐ(Aum)?
Almost every mantra begins with OM. The reason is given below.
The syllable Om is the root from which the Vedas have sprung. (Every rite, therefore, should commence with the utterance of that syllable of vast import). Of him who has uttered for him the syllables Om, Namas, Swaha, Svadha, and Vashat, and who has according to the extent of his ability, performed sacrifices, and other rites, there is no fear in respect of next life in all the three worlds.
Mahabharata Santi Parva Section CCLXVIII
One notable exception is the Rama Taraka Mantra which does not begin with OM.
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