$$ \operatorname{HCF}(a, 24)=1 $$ Now, $24=2^2 .3$ $\rightarrow \alpha$ is not the multiple of 2 or 3 Sum of values of $\alpha$ $$ \begin{aligned} & =S(U)-\{S(\text { multiple of } 2)+S \text { (multiple of } 3)-S(\text { multiple of } 6)\} \\ & =(1+2+3+\ldots \ldots 100)-(2+4+6 \ldots \ldots+100)-(3+6+\ldots . .99)+(6+12+\ldots . . .+96) \\ & =\frac{100 \times 101}{2}-50 \times 51-\frac{33}{2} \times(3+99)+\frac{16}{2}(6+96) \\ & =5050-2550-1683+816=1633 \text { Ans. } \end{aligned} $$