# Find the LCM of the given polynomial. x^{2}+4x+4, x^{3}+2x^{2}, (x+2)^{3}

Find the LCM of the given polynomial.
${x}^{2}+4x+4,{x}^{3}+2{x}^{2},{\left(x+2\right)}^{3}$
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Step 1
The given polynomials are,
${x}^{2}+4x+4,$
${x}^{3}+2{x}^{2},$
${\left(x+2\right)}^{3}$
We need to find the LCM of the given polynomials.
Step 2
On factorizing the first polynomial, we get
${x}^{2}+4x+4={x}^{2}+2x\cdot 2+{2}^{2}$
$={\left(x+2\right)}^{2}$
On factorizing the second polynomial, we get
${x}^{3}+2{x}^{2}={x}^{2}\left(x+2\right)$
And the third polynomial is ${\left(x+2\right)}^{3}$
The lowest common multiple of the three polynomials is the polynomial which is multiple of the given three polynomials,
Therefore, the LCM of the polynomials is ${x}^{2}{\left(x+2\right)}^{3}$