Magic Triangles in a Hexagon

    A - B - C
   / \ / \ / \
  D - E - F - G
 / \ / \ / \ / \
H - I - J - K - L
 \ / \ / \ / \ /
  M - N - O - P
   \ / \ / \ /
    Q - R - S
Place the numbers 1-19 in the hexagon, such that each of the twelve triangles of six numbers have the same sum. These include triangles such as ABCEFJ and BEFIJK. What are the lowest and highest possible common sums?

Extension: Find a solution which also has these sets equal to the common sum: the six corners (ACHLQS), the six sides (BDGMPR), and the six central values (EFIKNO).

For ease in comparing solutions, place the lowest-valued corner at A, and the lowest adjacent side at B. I know a computer can help solve this, but I'd be interested in any analytical approaches that can be found.

Source: Original.

Solution
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