Question

Find the LCM of the following: $66a^4{b}^2{c}^3,44a^3{b}^4{c}^2,24a^2{b}^3{c}^4$

• A. $264a^4{b}^4{c}^4$
• B. $24a^4{b}^4{c}^4$
• C. $246a^4{b}^4{c}^4$
• D. None of these

Answer 1

The correct option is A $264a^4{b}^4{c}^4$

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 $66a^4{b}^2{c}^3,44a^3{b}^4{c}^2$ and $24a^2{b}^3{c}^4$ as shown below:

$66a^4{b}^2{c}^3=2\times 3\times 11\times a\times a\times a\times a\times b\times b\times c\times c\times c44a^3{b}^4{c}^2=2\times 2\times 11\times a\times a\times a\times b\times b\times b\times b\times c\times c24a^2{b}^3{c}^4=2\times 2\times 2\times 3\times a\times a\times b\times b\times b\times c\times c\times c\times c$

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

$2\times 2\times 2\times 3\times 11\times a\times a\times a\times a\times b\times b\times b\times b\times c\times c\times c\times c=264a^4{b}^4{c}^4$

Hence, the LCM of $66a^4{b}^2{c}^3,44a^3{b}^4{c}^2$ and $24a^2{b}^3{c}^4$ is $264a^4{b}^4{c}^4$.