Another snippet, from the latest public draft of the System V x86-64 ABI [1]:

"""Structures and unions assume the alignment of their most strictly aligned compo- nent. Each member is assigned to the lowest available offset with the appropriate alignment. The size of any object is always a multiple of the object‘s alignment."""

I'd be fine with using the largest alignment, as above, instead of computing an lcm;  I can't believe it'll ever make a difference in practice.  For an empty struct (not allowed in C99, but allowed as a gcc extension, and allowed by the struct module), the alignment would be 1, of course.

[1] http://www.x86-64.org/documentation/abi.pdf