utmost, most, extreme
最 centers on the highest degree of something: the utmost, the most, or the extreme end of a scale.
recently; lately; these days; nowadays; right now
end; conclusion
beginning; outset; first; onset
best; supreme; wonderful; finest
last; final; closing
biggest; greatest; largest; maximum
most; extremely
latest; newest; late-breaking (news)
least; lowest; minimum
worst
strongest
already; now
most suitable; optimum; optimal; best
(in) the middle of; (in) the midst of; (in) the course of; (at) the height of
minimum
one's last moment; one's death; one's end
smallest (in size, degree, etc.); least; minimum; minimal
most (numerous); largest (number of)
cutting edge; leading edge; forefront; state of the art
maximum
shortest
Supreme Court
the very best; utmost
minimum; lowest; minimal; least
最 originally combined 冃 (a cap or covering) with 取 (to take), suggesting the idea of taking the topmost or covering everything, which developed into the sense of 'utmost' or 'most'. The modern form has 日 on top, which is a simplification of the original cap element.
The sun 日 sits above a hand taking something 取, as if reaching for the highest point: the utmost, the most extreme.
For サイ, imagine a sigh of relief when you finally reach the utmost peak: sigh -> サイ, and you are at the very top.