One event anchors this root: birth. The mother gives birth (לָלֶדֶת), the baby is born (לְהִוָּלֵד), the midwife delivers it (לְיַלֵּד), three binyanim for the three roles around one cradle. From there come the child, the boy and girl, the birth rate, even the birthday (יוֹם הֻלֶּדֶת). The initial י is weak: it drops in some forms and reappears in others. Every word here is verified against pealim, niqqud included.
The same root runs through the verb system. Each binyan is a voice: it bends the one idea into active, passive, causative or reciprocal. Tap to hear.
A perfect three-way split around one event. The pa'al is the mother's act (to give birth), the nif'al is the passive partner (to be born), and the pi'el is the helper's act (to deliver, what a midwife does). One birth, three points of view, three binyanim.
Same root letters, different noun moulds (mishkalim). The mould tells you the function: who does it, the act of doing it, or the thing produced.
Strip the prefixes, suffixes and vowels. Three consonants remain, and the meaning lives there.