Let $A=\{n\in N:H.C.F.(n,45)=1\}$ and
Let $\mathrm{B}=\{2\mathrm{k}:\mathrm{k}\in \{1,2,\dots ,100\left\}\right\}$. Then the sum of all the elements of $\mathrm{A}\cap \mathrm{B}$ is

Sum of elements  in $\mathrm{A}\cap \mathrm{B}$=$\begin{array}{l}=\underset{\text{Multiple of }2}{\underbrace{(2+4+6+\dots +200)}}-\underset{\text{Multiple of }2\text{ \& }3\text{ i.e. }6}{\underbrace{(6+12+\dots +198)}}\\ -\underset{\text{Multiple of }5\mathrm{\&}2\text{ i.e. }10}{\underbrace{(10+20+\dots +200)}}+\underset{\text{Multiple of }2,5\text{ \& }3\text{ i.e. }30}{\underbrace{(30+60+\dots +180)}}\\ =5264\end{array}$