Answer:
The LCM is:

Explanation:
To find the least common multiple (LCM) of 4x^2y and 12xy^2z, we need to determine the highest power of each variable that appears in either expression.
Let's break down the given expressions into their prime factors:

Now, we can identify the highest power of each prime factor:
2: Appears with a power of 2 in both expressions.
3: Appears with a power of 1 in the second expression only.
x: Appears with a power of 2 in the first expression only.
y: Appears with a power of 2 in the second expression only.
z: Appears with a power of 1 in the second expression only.
To find the LCM, we take the highest power of each prime factor:
LCM =

Therefore, the LCM of 4x^2y and 12xy^2z is 12x^2y^2z.
Hope it helps!