Question

Find the LCM of the following: $a^{m+1},a^{m+2},a^{m+3}$

• A. $a^{m+3}$
• B. $a^{m+2}$
• C. $a^{m+1}$
• D. None of these

Answer 1

The correct option is A $a^{m+3}$

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 $a^{m+1},a^{m+2}$ and $a^{m+3}$ as shown below:

$a^{m+1}=a^m\times a^1=a^m\times a{a}^{m+2}=a^m\times a^2=a^m\times a\times a{a}^{m+3}=a^m\times a^3=a^m\times a\times a\times a$

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

$a^m\times a\times a\times a=a^m\times a^3=a^{m+3}$

Hence, the LCM of $a^{m+1},a^{m+2}$ and $a^{m+3}$ is $a^{m+3}$.