Question

Pls give step by step solution please ​

Answer 1

Answer:

$lcm=4 x(x + 2)( {x - 2)}^{2} (x - 3).$

Step-by-step explanation:

$( {x}^{3} - 4x) = x( {x}^{2} - 4) = x(x - 2)(x + 2) \\ \\ 4( {x}^{2} - 5x + 6) = 4(x - 2)(x - 3) \\ \\ ( {x}^{2} - 4x + 4) = (x - 2)( x- 2) \\ \\ hcf = (x - 2) \\ \\ lcm = \frac{x(x - 2)(x + 2)4(x - 2)(x - 3)(x - 2)( x- 2)}{hcf} \\ \\ = \frac{x(x - 2)(x + 2)4(x - 2)(x - 3)(x - 2)( x- 2)}{(x - 2)} \\ \\ =4 x(x + 2)( {x - 2)}^{2} (x - 3). \\ \\ lcm =4 x(x + 2)( {x - 2)}^{2} (x - 3).$