Question

Find the LCM of the following

Answer 1

Least Common Multiple(LCM): The least common multiple of two or more algebraic expressions is the expression of lowest degree which is divisible by each of them without remainder.

LCM OF POLYNOMIALS :
1•Find the LCM of the numerical coefficient of the polynomials.
2•Factorise the given polynomials.
3•Take the highest power of each of the factors (including the ones in common)]
4•The product of the number and the powers of the factors obtained in step 1 and 3 is the LCM of the given polynomials.

SOLUTION:

•2x² - 18y² = 2 (x² - 9y²)
= 2 (x² - (3y)²)
[(a² - b²) = (a +b) (a -b)]
= 2 (x + 3y) (x - 3y)

•5x²y + 15xy² = 5xy (x +3 y)

•x³ + 27y³ = x³ + (3y)³
= (x + 3 y) (x² + x (3y) + (3y)²)
[(a³ + b³) = (a+b)(a²+ab+b²)]
= (x + 3y) (x² + 3 xy + 9y²)

L.C.M = 2 (x + 3y) x( 5 xy) x (x² + 3 xy + 9 y²)
[On taking the highest power of each of the factors (including the ones in common)]
L.C.M = 10xy (x + 3y) (x² + 3xy + 9y²)

Hence, the L.C.M is 10xy (x + 3y) (x² + 3xy + 9y²)

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Answer 2

Solution:-

given by :-
$p(x) = 2 {x}^{2} - 18 {y}^{2} \\ = 2( {x}^{2} - {(3y )}^{2} ) \\ \\ = 2(x + 3y)(x - 3y) \\ q(x) = 5 {x}^{2} y + 15x {y}^{2} \\ = 5xy(x + 3y) \\ r(x) = {x}^{3} + 27 {y}^{3} \\ = (x + y)( {x}^{2} + 9xy + 9 {y}^{2} ) \\ \\ lcm = 10xy(x + 1)(x + 3y)(x - 3y)( {x}^{2} + 9xy + 9 {y}^{2} )$
LCM = ●The LCM is the least common multiple or lowest common multiple between two or more numbers. We can find the least common multiple by breaking down each number into its prime factors.●

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