Question

if the hcf and LCM of two positive integer a and b are x and y respectively then x^2*y^2/a^2*b^2=​

Answer 1

Answer:

$\frac{ {x}^{2} {y}^{2} }{ {a}^{2} {b}^{2} } = 1$

Explanation:

Given,

HCF of a & b = x

LCM of a & b = y

Now,

By LCM & HCF relation formula,

LCM × HCF of the numbers = Product of the Numbers

i.e.,

$xy = ab$

-------------------(1)

Then,

$\: \: \: \: \: \frac{ {x}^{2} {y}^{2} }{ {a}^{2} {b}^{2} }$

$= \frac{ {(x}{y})^{2} }{ {(a} {b)}^{2} }$

$= {( \frac{ {x}{y}}{ab} )}^{2}$

$= {1}^{2}$--------------[from eqn (1)]

$= 1$