Question

Find the LCM of the following: $a^{2}bc,b^{2}ac,c^{2}ab$

• A. $a^2{b}^2{c}^2$
• B. $a^2{b}^3{c}^2$
• C. $a^3{b}^2{c}^2$
• D. None of these

Answer 1

The correct option is A $a^2{b}^2{c}^2$

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 $a^{2}bc,b^{2}ac$ and $c^{2}ab$ as shown below:

$a^{2}bc=a\times a\times b\times c{b}^{2}ac=b\times b\times a\times c{c}^{2}ab=c\times c\times a\times b$

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

$a\times a\times b\times b\times c\times c=a^2{b}^2{c}^2$

Hence, the LCM of $a^{2}bc,b^{2}ac$ and $c^{2}ab$ is $a^2{b}^2{c}^2$.