find the LCM of 11(t-7) and 77(t-7)

To find the LCM (Least Common Multiple) of two expressions, we can first simplify the expressions and then find their LCM. Let's simplify the expressions 11(t-7) and 77(t-7).

First, let's expand the expressions:
11(t-7) = 11t - 77
77(t-7) = 77t - 539

Now, let's find the LCM of these two simplified expressions.

To find the LCM, we need to find the common multiples of the two expressions. Let's list the first few multiples of each expression:

Multiples of 11t - 77:
11t - 77, 22t - 154, 33t - 231, 44t - 308, 55t - 385, ...

Multiples of 77t - 539:
77t - 539, 154t - 1078, 231t - 1617, 308t - 2156, 385t - 2695, ...

Looking at the multiples, we can see that the expression (11t - 77) repeats itself every time (t - 7) goes into the multiple. Similarly, the expression (77t - 539) repeats itself every time (t - 7) goes into the multiple.

Now, let's find the least common multiple (LCM) by finding the smallest multiple that both expressions share:

We see that (11t - 77) repeats itself when (t - 7) goes into any multiple of (77t - 539).

Thus, the LCM of 11(t-7) and 77(t-7) is (77t - 539).

Therefore, the LCM of 11(t-7) and 77(t-7) is 77t - 539.