Question

Find HCF and LCM of 404 and 96 and verify that HCF x LCM =Product of the two give numbers.​

Answer 1

Answer:

Step-by-step explanation:

Here, 404 = 2 × 2 × 101

And  96 = 2 × 2 × 2 × 2 × 2 × 3

Common factors = 2 × 2  

Therefore, HCF of 404 and 96 = 2 × 2 = 4

LCM of 404 and 96 = 2 × 2 × 2 × 2 × 2 × 3 × 101 = 9696

Now, HCF × LCM = 4 × 9696 = 38784

And product of the two numbers = 404 × 96 = 38784

Hence, it is verified. HCF × LCM = Product of 404 and 96.

Answer 2

Answer :-

LCM of 404 and 96 :

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

LCM = 2 × 2 × 101 × 2 × 2 × 2 × 3

$\implies$ 9696

$\boxed{\sf{\red{LCM = 9696}}}$

HCF of 404 and 96 :

Prime Factorization of 404

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

Prime Factorization of 96

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

404 = 2 × 2 × 101

96 = 2 × 2 × 2 × 2 × 2 × 3

HCF = 2 × 2 = 4

$\boxed{\sf{\red{HCF = 4}}}$

$\therefore$ The LCM is 9696 and HCF is 4

Verification of the Relation of HCF and LCM :

$\boxed{\sf{LCM \times HCF = Product\:of\:2\:numbers}}$

The numbers = 404 and 96

HCF = 4

LCM = 9696

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

$\sf{\implies}38784 = 38784$

We got both the sides equal when we placed the numbers and solved according to the formula.

Hence,

Verified !!

$\therefore$ It is verified.