Question

PLEASE HELPPPPP!!!!!!!!! (show work if you can)

Answer 1

`\mathrm{Factor\:}18x^4y^3z= 2\cdot \:3^2\cdot \:x^4\cdot \:y^3\cdot \:z\\\\\mathrm{Factor\:}30xy^2z^2= 2\cdot \:3\cdot \:5\cdot \:x\cdot \:y^2\cdot \:z^2\\\\\mathrm{Factor\:}12x^3y^2= 2^2\cdot \:3\cdot \:x^3\cdot \:y\\\\\mathrm{Multiply\:each\:factor\:with\:the\:highest\:power}= 2^2\cdot \:3^2\cdot \:5\cdot \:x^4\cdot \:y^3\cdot \:z^2\\\\180x^4y^3z^2`

Answer 2

`180x^4y^3z^2`

Explanation:

Start by finding the LCM of the coefficients of each polynomial:

`LCM(12,18,30)=180`

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 (
`x`,
`y`, and
`z`). The largest term of
`x` is
`x^4` in the first polynomial, so we'll take exactly that for our
`x` term in the LCM, absolutely nothing more. Similarly, the largest term of
`y` in any of the three polynomials is
`y^3` (also in the first polynomial) and the largest
`z` term in any of the three polynomials is
`z^2` in the second polynomial. Thus, the LCM of all our polynomials is:

`180\cdot x^4\cdot y^3\cdot z^2=\boxed{180x^4y^3z^2}`