Why is the Long Run Average Cost (LRAC) curve not obtained by combining the the minima of each short-run average cost curve?

The long-run average cost curve is also called the envelope curve as it is formed by enveloping the short-run cost curves corresponding to the different levels of output. In the long-run, the factors of production vary with the level of output produced. The long-run average cost curve is U-shaped which in the initial stage decreases, reaches a minimum point and after that, it increases. On the falling portion, the long-run curve intersects at the falling portion of the short-run average cost curve. It is because corresponding to that level of output a firm can produce by operating a specific plant that is relatively inexpensive to the other plants. It means that the short-run cost of that plant corresponding to a given level of output will be relatively less to any other plant used in the production.