Answer:
[tex]180x^4y^3z^2[/tex]
Step-by-step explanation:
Start by finding the LCM of the coefficients of each polynomial:
[tex]LCM(12,18,30)=180[/tex]
Next, to find the least common multiple of each of the following terms, we need to take the absolute minimum we can of each term ([tex]x[/tex], [tex]y[/tex], and [tex]z[/tex]). The largest term of [tex]x[/tex] is [tex]x^4[/tex] in the first polynomial, so we'll take exactly that for our [tex]x[/tex] term in the LCM, absolutely nothing more. Similarly, the largest term of [tex]y[/tex] in any of the three polynomials is [tex]y^3[/tex] (also in the first polynomial) and the largest [tex]z[/tex] term in any of the three polynomials is [tex]z^2[/tex] in the second polynomial. Thus, the LCM of all our polynomials is:
[tex]180\cdot x^4\cdot y^3\cdot z^2=\boxed{180x^4y^3z^2}[/tex]
