Question

The LCM of 8 x^4 y^2 and 48 x^2 y^ 4 is​

Answer 1

Answer:

d the LCM of the following

(i) 8x4y2, 48x2y4

(ii) 5x -10, 5x2 – 20

(iii) x 4 -1, x 2 − 2x + 1

(iv) x 3 - 27, (x - 3)2, x 2 – 9

Solution

(i) 8x 4y2, 48x 2y4

First let us find the LCM of the numerical coefficients.

That is, LCM (8, 48) = 2 × 2 × 2 ×6 = 48

Then find the LCM of the terms involving variables.

That is, LCM (x 4y2, x 2y4 ) = x 4y4

Finally find the LCM of the given expression.

We condclude that the LCM of the given expression is the product of the LCM of the numerical coefficient and the LCM of the terms with variables.

Therefore, LCM (8x 4y2, 48x 2y4 ) = 48x 4y4

Answer 2

Answer:

The L.C.M of $8x^4y^2$ and $48x^2y^4$ is $48x^4y^4$.

Step-by-step explanation:

LCM is the method of finding the smallest possible multiple of two or more numbers. LCM stands for Least common multiple.

An algebraic expression consisting of only term is termed as monomials.

Consider the first monomial as follows:

$8x^4y^2$

⇒ 8 × $x^4$ × $y^2$

Factorisation of the number 8 is

8 = 2 × 2 × 2

Factorisation of the expression $x^4$ is

$x^4=x$ × $x$ × $x$ × $x$

Factorisation of the expression $y^2$ is

$y^2=y$ × $y$

Hence, the factorisation of the monomial $8x^4y^2$ is

$8x^4y^2=$ 2 × 2 × 2 × $x$ × $x$ × $x$ × $x$ × $y$ × $y$

Similarly,

Consider the second monomial as follows:

$48x^2y^4$

⇒ 48 × $x^2$ × $y^4$

Factorisation of the number 8 is

48 = $2$ × $2$ × $2$ × $2$ × $3$

Factorisation of the expression $x^2$ is

$x^2=x$ × $x$

Factorisation of the expression $y^4$ is

$y^4=y$ × $y$ × $y$ × $y$

Hence, the factorisation of the monomial $48x^2y^4$ is

$48x^2y^4=$ $2$ × $2$ × $2$ × $2$ × $3$ × $x$ × $x$ × $y$ × $y$ × $y$ × $y$

Now,

The L.C.M of $8x^4y^2$ and $48x^2y^4$ is

⇒ $2$ × $2$ × $2$ × $2$ × $3$ × $x$ × $x$ × $x$ × $x$ × $y$ × $y$ × $y$ × $y$

⇒ $48x^4y^4$

Therefore, the L.C.M is $48x^4y^4$.

SPJ3