Math, asked by Goldy4728, 1 year ago

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

Answers

Answered by brijeshattri1603
4

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:


Answered by Avengers00
18
\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}}}}
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