Question

Find HCF and LCM of 404and 96 and verify that HCF into LCM = product of the given two numbers

Answer 1

$\huge{\bf{\underline{\red{Solution :}}}}$

$\boxed{\bold{\red{First \ Case : LCM}}}$

⇒LCM of 404 and 96

$\begin{array}{r | l}2 & 404 , 96 \\\cline{2-2} 2 & 202 , 48 \\\cline{2-2} 2 & 101 , 24 \\\cline{2-2} 2 & 101 , 12 \\\cline{2-2} 2 & 101 , 6 \\\cline{2-2} 3 & 101 , 3 \\\cline{2-2} 101& 101 , 1 \\\cline{2-2} & 1\end{array}$

LCM = $\bold{2^{5} \times 3 \times 101}$

LCM = $\boxed{\bold{9696}}$

$\boxed{\bold{\red{Second \ Case : HCF}}}$

⇒HCF of 404 and 96

Firstly HCF of 404 :-

$\begin{array}{r | l}2 & 404 \\\cline{2-2} 2 & 202 \\\cline{2-2} 101 & 101 \\\cline{2-2} & 1\end{array}$

Now HCF of 96 :-

$\begin{array}{r | l}2 & 96 \\\cline{2-2} 2 & 48 \\\cline{2-2} 2 & 24 \\\cline{2-2} 2 & 12 \\\cline{2-2} 2 & 6 \\\cline{2-2} 3 & 3 \\\cline{2-2} & 1\end{array}$

∴404 = 2 x 2 x 101

96 = 2 x 2 x 2 x 2 x 2 x 3

HCF = 2 x 2 = 4

According to Question :

$\implies \bold{HCF \times LCM = 404 \times 96}$

$\implies \bold{ 4 \times 9696 = 404 \times 96}$

$\implies \bold{38,784 = 38,784}$

⇒So verified that LHS = RHS so product of HCF and LCM is equal to given number product

$\rule{200}2$