\(k > 0\) & divisible by \(225\) & \(216\)

\(k=(2^a)*(3^b)*(5^c)\)

We need to find the least value of \(a+b+c\)

For that, we need to find the \(lcm\) of \(225\) & \(216\)
\(225 = 5^2 * 3^2\)

\(216 = 2^3 * 3^3\)

\(LCM = 2^3 * 3^3 * 5^2\)

As \(k\) is divisible by \(225\) & \(216\), it will also be divisible by the \(lcm\) by which we can get the least sum of \(a + b + c\)

\(LCM = 2^3 * 3^3 * 5^2\) comparing with \(k=(2^a)*(3^b)*(5^c)\)

\(a = 3, b = 3, c = 2\)

The least sum of\( a + b + c = 8\)

Answer E