Here are a number of renderings of Genesis 21:6. First, the Hebrew (MT):
וַתֹּאמֶר שָׂרָה צְחֹק עָשָׂה לִי אֱלֹהִים כָּל־הַשֹּׁמֵעַ יִֽצְחַק־לִֽי׃
The LXX: “εἶπεν δὲ Σαρρα γέλωτά μοι ἐποίησεν κύριος ὃς γὰρ ἂν ἀκούσῃ συγχαρεῖταί μοι”
The Vulgate: “dixitque Sarra risum fecit mihi Deus quicumque audierit conridebit mihi”
And finally, the good old AV: “And Sarah said, God hath made me to laugh, [so that] all that hear will laugh with me” (KJV).
The first bit of Hebrew is straightforward enough: “וַתֹּאמֶר שָׂרָה צְחֹק עָשָׂה לִי אֱלֹהִים”
“And Sarah said, “God made laughter unto me (“le + a 1st sing., poss. pronoun). The second bit of Hebrew is straightforward as well: כָּל־הַשֹּׁמֵעַ יִֽצְחַק־לִֽי
“Everyone who hears will laugh because of me” (here taking le in a purposive sense).
What’s fascinating about all three translations is the degree to which all supply causal relations between the two clauses. The LXX and AV are most obtrusive in this regard: “gar an,” “so that,” though the AV uses brackets to note that this is an interpretive bridge. The Latin more or less mimics the Hebrew’s terseness: were I rendering the Latin into English, I think I would make each clause its own sentence.
Nonetheless, the Greek is probably a fine rendering of the actual intent of the Hebrew — it’s just that the relation between the two clauses has to be deduced within the syntactical desolation that is the MT.