If $a=2^{2} imes 3^{x}, b=2^{2} imes 3 imes 5, c=2^{2} imes 3 imes 7$ and $\operatorname{L

Question

If $a=2^{2} 	imes 3^{x}, b=2^{2} 	imes 3 	imes 5, c=2^{2} 	imes 3 	imes 7$ and $\operatorname{LCM}(a, b, c)=3780$, then $x$ is equal to\

Professor PC Thomas Classes · Answer

(c): We have, $a=2^{2} 	imes 3^{x}, b=2^{2} 	imes 3 	imes 5, c=2^{2} 	imes 3 	imes 7$\ $\operatorname{LCM}(a, b, c)=2^{2} 	imes 3^{x} 	imes 5 	imes 7$\ $\Rightarrow \quad 2^{2} 	imes 3^{x} 	imes 5 	imes 7=3780$\ ( ∵ Given)\ $\Rightarrow 140 	imes 3^{x}=3780 \Rightarrow 3^{x}=27 \Rightarrow 3^{x}=3^{3}$\ $	herefore \quad x=3$\