To find the LCM (Least Common Multiple) of 12x and 36x, we can first factor each expression:
12x = 2^2 * 3 * x
36x = 2^2 * 3^2 * x
The LCM is the product of the highest powers of all prime factors involved. In this case, the prime factors are 2, 3, and x.
The highest power of 2 is 2^2, which appears in both factorizations.
The highest power of 3 is 3^2, which only appears in the factorization of 36x.
The highest power of x is x, which appears in both factorizations.
Therefore, the LCM of 12x and 36x is:
LCM(12x, 36x) = 2^2 * 3^2 * x = 36x
So the LCM of 12x and 36x is 36x.