47 After all, however, this explanation may also be suggested—namely, that in the first instance the Lord, along with His disciples and no others, was on some more elevated portion of the mountain, and that during the period of His stay there He chose out of the number of His followers those twelve; that then He came down in company with them, not indeed from the mountain itself, but from that said altitude on the mountain, into the plain— that is to say, into some level spot which was found on the slope of the mountain, and which was capable of accommodating great multitudes; and that thereafter, when He had seated Himself, His disciples took up their position next Him, and in these circumstances He delivered both to them and to the other multitudes who were present one discourse, which Matthew and Luke have both recorded, their modes of narrating it being indeed different, but the truth being given with equal fidelity by the two writers in all that concerns the facts and sayings which both of them have recounted.
For we have already prefaced our inquiry with the position, which indeed ought of itself to have been obvious to all without the need of any one to give them counsel to that effect beforehand, that there is not [necessarily] any antagonism between writers, although one may omit something which another mentions; nor, again, although one states a fact in one way, and another in a different method, provided that the same truth is set forth in regard to the objects and sayings themselves.
In this way, therefore, Matthew's sentence, “Now when He had come down from the mountain,” may at the same time be understood to refer also to the plain, which there might very well have been on the slope of the mountain. And thereafter Matthew tells the story of the cleansing of the leper, which is also given in a similar manner by Mark and Luke.
Source: The Harmony of the Gospels (New Advent)