Additional note (June, 2022):

Subclause 6.7.3 [basic.align] paragraph 4 specifies:

... Every alignment value shall be a non-negative integral power of two.

Thus, the situation that a stricter alignment is not an integral multiple of a weaker alignment does not arise.

Requirements for the alignment of pointers returned by new-expressions are given in 7.6.2.8 [expr.new] paragraph 10:

For arrays of char and unsigned char, the difference between the result of the new-expression and the address returned by the allocation function shall be an integral multiple of the most stringent alignment requirement (6.8 [basic.types]) of any object type whose size is no greater than the size of the array being created.

The intent of this wording is that the pointer returned by the new-expression will be suitably aligned for any data type that might be placed into the allocated storage (since the allocation function is constrained to return a pointer to maximally-aligned storage). However, there is an implicit assumption that each alignment requirement is an integral multiple of all smaller alignment requirements. While this is probably a valid assumption for all real architectures, there's no reason that the Standard should require it.

For example, assume that int has an alignment requirement of 3 bytes and double has an alignment requirement of 4 bytes. The current wording only requires that a buffer that is big enough for an int or a double be aligned on a 4-byte boundary (the more stringent requirement), but that would allow the buffer to be allocated on an 8-byte boundary — which might not be an acceptable location for an int.

Suggested resolution: Change "of any object type" to "of every object type."

A similar assumption can be found in 7.6.1.10 [expr.reinterpret.cast] paragraph 7:

...converting an rvalue of type "pointer to T1" to the type "pointer to T2" (where ... the alignment requirements of T2 are no stricter than those of T1) and back to its original type yields the original pointer value...

Suggested resolution: Change the wording to

...converting an rvalue of type "pointer to T1" to the type "pointer to T2" (where ... the alignment requirements of T1 are an integer multiple of those of T2) and back to its original type yields the original pointer value...

The same change would also be needed in paragraph 9.