Why warships carried layered anti-aircraft batteries

What was the purpose of combining 105-millimeter, 37-millimeter, and 20-millimeter anti-aircraft guns on one ship?

The different weapons could engage different targets and ranges, with their coverage intended to reinforce one another.

A mixed anti-aircraft battery created a layered defense. Heavier weapons could reach farther, while smaller mounts supplied faster and closer fire. Overlapping envelopes gave the ship more ways to engage an aircraft as it approached. The arrangement depended on integration across ranges, ammunition, and fire-control tasks rather than one universal caliber.