I saw the following sentence:
Моя бабушка умерла в 1959 году, не дожив до ста лет всего лишь трёх месяцев.
I understood the meaning of this sentence. "My grandmother (...) lived three months short of 100".
However, I don't get the syntax in this sentence. What's the meaning of the genitive трёх месяцев here? Does it imply "for a matter of three months"?