Find the number of ordered triples $$(𝑎, 𝑏, 𝑐)$$ of positive integers such that $$1 \neq 𝑎, 𝑏, 𝑐 \neq 50$$ which satisfy the relation
$$\frac{lcm(a,c)+lcm(b,c)}{a + b} = \frac{26c}{27}$$.
Here, by $$lcm(𝑥, 𝑦)$$ we mean the $$LCM$$, that is, least common multiple of $$𝑥$$ and $$𝑦$$.