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.

QUESTION :
Find the LCM of the following
(x + 4)² ( x - 3)³ , ( x - 1) (x + 4) (x - 3)²

SOLUTION:
•(x + 4)² ( x - 3)³
• ( x - 1) (x + 4) (x - 3)²

L.C.M = (x + 4)² (x - 3)³ (x - 1)
[On taking the highest power of each of the factors (including the ones in common)]

Hence ,the L.C.M is (x + 4)² (x - 3)³ (x - 1)

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Answer 2

solution:-

given by:-
$p(x) = {(x + 4)}^{2} {(x - 3)}^{3} \\ = (x + 4)(x + 4)(x - 3) {(x - 3)}^{2} \\ q(x) = (x - 1)(x + 4) {(x - 3)}^{2} \\ \\ lcm =(x - 1) {(x + 4)}^{2} ( {(x - 3)}^{3} ans$
lcm = product of highest  power of each prime factor involved in the numbers .

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