Question

Find the HCF of 96 and 404 by prime factorisation method amd hence find their LCM.​

Answer 1

$\huge\star{\underline{\mathtt{\red{A}\pink{n}\green{s}\blue{w}\purple{e}\orange{r}}}}$

$\longrightarrow$$\sf\pink{96=2×2×2×2×2×3={2}^{5}\times{3}^{1}}$

$\longrightarrow$$\sf\red{404=2×2×101={2}^{2}\times{101}^{1}}$

$\Large\sf\underline\green{Therefore,}$

$\longrightarrow$$\sf\purple{HCF\:=\:2\:×2\:=\:4}$

$\Large\sf\underline\orange{Also,}$

$\longrightarrow$$\sf\blue{HCF\:×\:LCM\:=\:product\:of\:2\:numbers}$

$\longrightarrow$$\sf\orange{4\:×\:LCM\:=\:96\:×\:404}$

$\longrightarrow$$\sf\pink{LCM= \frac{96 \times 404}{4}}$

$\longrightarrow$$\sf\red{LCM\:=\:96\:×\:101}$

$\longrightarrow$$\large\sf\green{LCM\:=\:9696}$

Answer 2

Answer:

$\boxed{HCF = 4}$

$\boxed{LCM = 9696}$

Explanation:

HCF of 96 and 404

For finding HCF of two given number by prime factorization , we must first prime factorize the given numbers

96 =  2 × 2 × 2 × 2 × 2 × 3

404 = 2 × 2 × 101

Next we must take common factors in the two numbers .(The common Factors are underlined)

∴ HCF = 2 × 2 = 4

LCM of 96 and 404

∵ We have the HCF of 96 and 404 , we can easily find the LCM of 96 and 404

HCF × LCM = Product of given numbers

We have ,

Numbers = 96 and 404

HCF = 4

$\implies$ 4 × LCM = 96 × 404

$\sf LCM = \dfrac{96*404}{4}$

$\sf LCM = \dfrac{38784}{4}$

LCM = 9696