Question

Using fundamental theorem theory of arithmetic find the LCM and HCF of 404 and 96

Answer 1

Answer:

First 404-2×2×101

96-2×2×2×2×2×3

So, hcf =2×2 =4

And lcm= 9696

We know that -hcf× lcm = product of two no.

4×9696=404×96

38785=38784

Step-by-step explanation:

Answer 2

$\underline{\underline{\Huge{\textbf{Solution:}}}}$

$\underline{\Large{\textsf{Step-1}}}$
Express 404 and 96 as Product of prime Factors.

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

$404 = 2 \times 2 \times 101$
$96\: = 2 \times 2 \times 2 \times 2 \times 2 \times 3$



$\underline{\Large{\textsf{Step-2}}}$
Note the Common Prime factors

Common Prime factors = 2, 2



$\underline{\Large{\textsf{Step-3}}}$
Find HCF of 404 and 96

We know,
$\bigstar \textbf{H.C.F\: is\: the\: Product\: of\: all\: common\: prime\: factors}$

$\textsf{HCF = 2 \times 2 = 4}$



$\underline{\Large{\textsf{Step-4}}}$
Find LCM using the Relation.
$\bigstar \textbf{HCF \times LCM = Product\: of\: the\: Numbers}$

On Substituting

$\implies 4 \times LCM = 404 \times 96$

$\implies LCM = \dfrac{404 \times 96}{4}$

$\implies LCM = 101 \times 96$

$\implies LCM = 96(100+1)$

$\implies LCM = 9600+96$

$\implies LCM = 9696$

$\therefore$
$\blacksquare \: \textsf{The HCF of 404 and 96 is \underline{\large{\textbf{4}}}}\\\blacksquare\: \textsf{The LCM of 404 and 96 is \underline{\large{\textbf{4}}}}$