LCM of (x-y) and 2(y-x)

To find the least common multiple (LCM) of two expressions, we need to factorize the expressions first.

Let's factorize the expressions (x-y) and 2(y-x):

(x-y) = -1(x-y)
2(y-x) = -2(x-y)

Notice that the two expressions have a common factor of (x-y) that is negative in one expression and positive in the other.

To find the LCM, we need to find the product of the expressions, but we don't multiply the common factor twice. Instead, we take the absolute value of the common factor.

Multiplying the expressions, we have:

LCM = |-1(x-y) × -2(x-y)|

Now, we can simplify this expression:

LCM = |2(x-y)^2|

Therefore, the LCM of (x-y) and 2(y-x) is 2(x-y)^2.

If you change the x and y to real numbers such as -2 and 3 the x-y=-5 and y-x=3--2=5 then multiply by 2 to get 10.

So, I would thin that the LCM might be
-2. Try it out in a few more weird number situations and see if it works.