Question

Plzzz solve this question

Find the HCf of the following numbers -

• 96 and 404

By using prime factorisation method and hence, find ther LCM


Plzz fastt​

Answer 1

$\large{\underline{\mathrm{\blue{Answer-}}}}$

HCF of 96 and 404 = 4

LCM of 96 and 404 = 9696

$\large{\underline{\mathrm{\blue{Explanation-}}}}$

†Prime factorisation of 96 :

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

Prime factors of 96 = 2 × 2 × 2 × 2 × 2 × 3

†Prime factorisation of 404 :

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

Prime factors of 404 = 2 × 2 × 101

__________________________

★ HCF of 96 and 404 :

$\implies$ HCF of 96 and 404 = 2 × 2

$\implies$ HCF of 96 and 404 = 4

_________________________

★ LCM of 96 and 404 :

We know that,

HCF × LCM = Product of given numbers

$\implies$ 4 × LCM = 96 × 404

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

$\implies$ LCM of 96 and 404 = 9696

Answer 2

QUESTION:-

Find the HCf of the following numbers -

• 96 and 404

By using prime factorisation method and hence, find ther LCM.

SOLUTION:-

IN A FIRST PART,

✡prime factorisation of 96.

2 | 96

2 | 48

2 | 24

2 | 12

2 | 6

2 | 3

3 | 3

| 1

⇰prime factors of 96 = 2 ×2×2×2×2×2×3

IN A SECOND PART,

✡prime factorisation of 404.

2 | 404

2 | 202

101 | 101

| 1

⇰ prime factors of 404 = 2×2 ×101

NOW,

✡ HCF of 96 and 404.

⇰ HCF of 96 and 404 = 2×2

⇰.°. HCF of 96 and 404 = 4 ------(1)

✡ LCM of 96 and 404.

⇰ HCF × LCM = product of given numbers. ---(formula)

⇰ 4 ×LCM = 96 ×404

⇰ LCM = 96 ×404 /4

⇰ .°. LCM = 38784/4

⇰.°. LCM of 96 and 404 is 9696.