Final answer:
The LCM of 18x^2y^3 and 24x^3y is found by factoring each expression, comparing the factors, and selecting the highest powers for each factor. The LCM is 72x^3y^3.
Step-by-step explanation:
To find the Least Common Multiple (LCM) of the given algebraic expressions 18x2y3 and 24x3y, we first need to factor each expression. The LCM of algebraic expressions is found by taking the highest powers of each variable from the expressions.
The expression 18x2y3 can be factored into 2 × 32 × x2 × y3, and the expression 24x3y can be factored into 23 × 3 × x3 × y. To find the LCM, we compare the factors, choosing the highest power for each factor that appears in any of the expressions.
The LCM will have the factors:
23 (since 23 is higher than 2),
32 (since 32 is higher than 3),
x3 (since x3 is higher than x2),
y3 (since y3 is higher than y).
Therefore, the LCM of 18x2y3 and 24x3y is 72x3y3.