Question

Find the LCM of the following: $x^3{y}^2,xyz$

• A. $x^3{y}^{2}z$
• B. $x^2{y}^{2}z$
• C. $x^3{y}^2{z}^2$
• D. None of these

Answer 1

The correct option is A $x^3{y}^{2}z$

We know that the least common multiple (LCM) is the smallest number or expression that is a common multiple of two or more numbers or algebraic terms.

We first factorize the given monomials $x^3{y}^2$ and $xyz$ as shown below:

$x^3{y}^2=x\times x\times x\times y\times yxyz=x\times y\times z$

Now multiply all the factors, using each common factor only once, therefore, the LCM is:

$x\times x\times x\times y\times y\times z=x^3{y}^{2}z$

Hence, the LCM of $x^3{y}^2$ and $xyz$ is $x^3{y}^{2}z$.