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To find the least common multiple (LCM) of 6x^2 and 12x, we first need to break down each term into its prime factors.
6x^2 can be broken down into 2 * 3 * x * x, while 12x can be broken down into 2 * 2 * 3 * x.
The LCM is the product of all the unique prime factors with the highest power they appear in any of the numbers, which in this case is 2 * 2 * 3 * x * x.
Therefore, the LCM of 6x^2 and 12x is 12x^2.
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