Question

L.C.M. of two numbers is 144 and their H.C.F. is 36
If one number is 48, the other number will be-​

Answer 1

Answer:

108

Step-by-step explanation:

Let one number be x

LCM × HCF = product of the numbers

144 × 36 = 48x

or, x=  5184/48 = 108

Therefore, the other number is 108.

Answer 2

$\begin{gathered} \frak{Given} \begin{cases} \sf{ LCM \: of \: two \: numbers = 144} \\ \sf{HCF \: of \: two \: numbers = 36} \\ \sf{One \: of \: the \: number = 48} \end{cases} \end{gathered}$

$\: \:$

$\begin{gathered} \frak{To \: Find} \begin{cases} \sf{ The \: other \: number} \end{cases} \end{gathered}$

$\: \:$

$\large{\frak{ \pmb{Solution :}}}$

$\sf{Let \: the \: other \: number \: be "x".}$

$\: \:$

$\sf{Now , applying \: the \: relation ;}$

$\: \:$

$\begin{gathered} \star \: {\boxed{\green{\sf{HCF \times LCM = Product \: of \: two \: numbers}}}} \end{gathered}$

$\: \:$

$\sf{Substituting \: the \: values \: we \: have ,}$

$\begin{gathered} \implies \sf \: 36 \times 144 = 48 \times x \end{gathered}$

$\begin{gathered} \implies \sf \: 5184 = 48 \times x \end{gathered}$

$\begin{gathered} \implies \sf \: x = \frac{5184}{48} \end{gathered}$

$\begin{gathered}\implies{\underline{\boxed{\red{ \sf{x = 108}}}}} \: \end{gathered}$

$\: \:$

$\star \: { \underline{ \boxed{ \frak{ \purple{Hence , the \: other \: number \: is 108.}}}}}$

$\: \:$