What is the lcm of 4x²(x-1) and 6x(x-1)?

The first step to find the LCM of 4x²(x-1) and 6x(x-1) is to find the LCM of 4x² and 6x. We can forget about the x-1 for now because, since it is common, we can factor it out of both for the LCM.

The LCM of 4x² and 6x is 12x².

Now that we have our two terms, we can use them to find the LCM. The LCM would be the product of these two terms, which is 12x²(x-1). 

4x²(x-1) and 6x(x-1)

We need to find all factors to find Least common multiple.

4x²(x-1) and 6x(x-1)

1) Both expressions have (x-1)
2) 4x²(x-1) and 6x(x-1)
First expression has x² and second one has x. We need to take the highest power. So, we will take x².
3) 4= 2*2 and 6=2*3
So, we need to take 2*2 ( to be acceptable for 4) and 3 (for 6), because we already have 2*2.
2*2*3

4) Altogether  we got, 2*2*3*x²(x-1)=12x²(x-1)
 
Answer : 12x²(x-1)
It can be written also as 12x³ -12x².