Find the least common multiple (LCM) of the expressions (15x^2y), (5xy^2), and (30x^3y^2).

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Step:1 ：First, decompose each expression into its prime factors. (15x^2y = 3*5*x*x*y), (5xy^2 = 5*x*y*y), and (30x^3y^2 = 2*3*5*x*x*x*y*y).Step:2 ：Then, for each factor, take the highest power that appears in any of the factorizations. Here, the factors are 2, 3, 5, x, and y. The highest powers are (2^1), (3^1), (5^1), (x^3), and (y^2).Step:3 ：Finally, multiply these highest powers together to get the least common multiple. The LCM is (2*3*5*x*x*x*y*y = 30x^3y^2).

Answer

Step: 1 ：First, decompose each expression into its prime factors. (15x^2y = 3*5*x*x*y), (5xy^2 = 5*x*y*y), and (30x^3y^2 = 2*3*5*x*x*x*y*y).Step: 2 ：Then, for each factor, take the highest power that appears in any of the factorizations. Here, the factors are 2, 3, 5, x, and y. The highest powers are (2^1), (3^1), (5^1), (x^3), and (y^2).Step: 3 ：Finally, multiply these highest powers together to get the least common multiple. The LCM is (2*3*5*x*x*x*y*y = 30x^3y^2).

Find the least common multiple (LCM) of the expressions \(15x^2y\), \(5xy^2\), and \(30x^3y^2\).

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