Final answer:
The least common multiple (LCM) of (a^4 + a^2b^2 + b^4) and (a^3 + b^3) is (a² + b²)(a + b)(a² - ab + b²).
Step-by-step explanation:
To find the least common multiple (LCM) of a⁴ + a²b² + b⁴ and a³ + b³, we need to factorize both expressions.
First, let's consider a⁴ + a²b² + b⁴. This expression can be factored as (a² + b²)(a² + b²).
Next, let's consider a³ + b³. This expression can be factored as (a + b)(a² - ab + b²).
Now, we can find the LCM by multiplying the highest power of each factor that appears in both expressions.
In this case, the LCM is (a² + b²)(a + b)(a² - ab + b²).