Question

how do I find the least common multiple of "14x^4y^6z^3" and "24x^6y^2z^8"

Answer 1

The given expressions are

$\begin{gathered} 14x^4y^6z^3 \\ 24x^6y^2z^8 \end{gathered}$

First, we look for the least common multiply for the numbers 14 and 24.

24 14 | 2

12 7 | 2

6 7 | 2

3 7 | 3

1 7 | 7

1 1

We have the product 2x2x2x3x7=168.

The least common multiple for the numbers is 168.

Now, we find the least common multiples for the variables.

The least common multiple of x variables is

$x^6$

The least common multiple for y variables.

$y^6$

The least common factor for z variables is

$z^8$

Remember that the least common multiple of variables is the one with the greatest exponent.

Therefore, the least common factor for the given expressions is

$168x^6y^6z^8$