What is the LCM of x⁴ + x²y² + y⁴, x³ + y³, x³ - y³?

Given:

 x4 + x2y2 + y4, x3 + y3, x3 - y3

Concept:

LCM: It is the product of the greatest power of each prime factor,

involved in the numbers.

Formula Used:

(a⁴ + a²b² + b⁴) = (a² + ab + b²)(a² - ab + b²)

(a2 - b2) = (a + b)(a - b)

(a³ - b³) = (a - b)(a² + ab + b²)

(a3 + b3) = (a + b)(a2 - ab + b2)

Calculation:

x⁴  + x²y² + y⁴ = (x2 + y2 - xy)(x2 + y2 + xy)

x3 + y3 = (x + y)(x² - xy + y²) 

x3 - y3 = (x - y)(x² + xy + y²)

LCM = (x + y)(x - y)(x² - xy + y²)(x²+ xy + y²)

LCM = (x² - y²)(x⁴ + x²y² + y⁴)

Again, we know that 

a³ - b³ = (a - b)(a² + ab + b²)

LCM = (x⁶ - y⁶)

∴ The correct answer is (x⁶ - y⁶).