Question

If 1125 = 3^m×5^n;find m and n ​

Answer 1

Given :

$1125 = {3}^{m} \: {5}^{n}$

To find :

find the value of m and n

Solution :

LCM of 1125 :

$\begin{array}{r | I} 5 & 1125 \\ \cline{2-2} 5 & 225 \\ \cline{2-2} 5 & 45 \\ \cline{2-2} 3 & 9 \\ \cline{2-2} 3 & 3 \\ \cline{2-2} & 1 \end{array}$

LCM = 5 x 5 x 5 x 3 x 3

$= > {5}^{3} \: {3}^{2}$

$= > 1125 = {3}^{2} \: {5}^{3}$

On Comparison, we get :

$= > {3}^{m} \: {5}^{n} = {3}^{2} \: {5}^{3}$

$= > m = 2 \: and \: n = 3$

Hence, the value of m=2 and n =3.