Solution

We have,

$45=3^2\times 5$

So, prime divisors of $45$ are $3$ and $5$.

Using Euler's phi function,

$\phi(45)=45\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{5}\right)$

$=45\times \dfrac{2}{3}\times \dfrac{4}{5}$

$=24$