Final answer:
The taxonomic category of 'phylum' includes the least closely related organisms as it is one of the broader levels in the hierarchical Linnaean system.
Step-by-step explanation:
The taxonomic category that would include the least closely related organisms is the phylum. In the hierarchical taxonomic classification system, also known as the Linnaean system, organisms are organized into groups that become increasingly broad; from species, the most specific level, to domain, the most inclusive level.
The hierarchy in order from most specific to least inclusive is: species, genus, family, order, class, phylum, kingdom, and domain. Therefore, the phylum encompasses a larger number of diverse organisms than other lower taxonomic levels like family, genus, or order, hence reflecting less close relatedness among the organisms within it.