find the LCM of (7 4z), (49-16zsquared), and (7-4z)

To find the LCM (Least Common Multiple) of the given expressions, we need to find their common factors and the highest power of each factor.

Let's begin by factoring each expression:

1. 7 - 4z:
The expression 7 - 4z is already factored, and it doesn't have any common factors.

2. 7 + 4z:
The expression 7 + 4z is already factored, and it doesn't have any common factors either.

3. 49 - 16z^2:
The expression 49 - 16z^2 can be factored as (7 - 4z)(7 + 4z). Here, the common factor is (7 - 4z).

Now, we need to identify the highest power of each common factor. In this case, the common factor is (7 - 4z).

The highest power of (7 - 4z) is 1, as it appears once in each expression.

Therefore, the LCM of (7 - 4z), (7 + 4z), and (49 - 16z^2) is:

LCM = (7 - 4z)(7 + 4z) = 49 - 16z^2