Let $n$ be the smallest number which is divisible by $x, y$ and $z$ and leaves remainder $r$ in each case.
So$, n = LCM ( x , y , z ) + r$
According to Question
$x = 20 , y = 42 , z = 76$ and $r = 7$
Smallest number, $n = LCM (20, 42, 76 ) + 7$
$\implies n = 7980 + 7 = 7987$
So, option (C) is the right choice