Let A = \ n ∈ N: H . C . F . (n, 45) = 1\ and let B = \ 2k: k ∈ \...

Here $B = \left\{2, 4, 6, 8 . . . . , 200\right\}$

Sum of elements in $A \cap B$

$= \mathop{\mathop{\left(2 + 4 + 6 + \ldots + 200\right)}_{⏟}}_{Multipleof 2} - \mathop{\mathop{\left(6 + 12 + \ldots + 198\right)}_{⏟}}_{Multipleof2 \text{ and } 3i . e . 6}$

$- \mathop{\mathop{\left(10 + 20 + \ldots + 200\right)}_{⏟}}_{Multipleof5 \text{ and } 2i . e . 10} + \mathop{\mathop{\left(30 + 60 + \ldots + 180\right)}_{⏟}}_{Multipleof2, 5 \text{ and } 3i . e . 30}$

$= 2\left(\dfrac{100 \times 101}{2}\right) - 6\left(\dfrac{33 \times 34}{2}\right) - 10\left(\dfrac{20 \times 21}{2}\right) + 30\left(\dfrac{6 \times 7}{2}\right)$

$= 5264$