Question

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

Answer 1

let a = 494 ; b = 96

Expressing the number as a product of prime number

404=2×2×101

96=2×2×2×2×2×3

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

∴ HCF of 404 =2×2×10196=2×2×2×2×2×3

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

∴ HCF of 404 and 96 is 2×2=4Now HCF×LCM=4×9696=38784

Product of two given numbers 404×96=38784

Hence HCM×LCM= product of two given numbers.

thank you ❤️

Answer 2

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

$\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}$