What is the least common multiple of the expressions 4(xy)2
and 3(x)3y
?
Responses
(x2)y
open paren x squared close paren times y
(x6)(y2)
open paren x to the 6th power close paren times open paren y squared close paren
12(x3)(y2)
12 open paren x cubed close paren open paren y squared close paren
12(x6)(y2)
The least common multiple of the expressions 4(xy)^2 and 3(x)^3y is 12(x^3)(y^2).
To find the least common multiple (LCM) of the expressions 4(xy)2 and 3(x)3y, we need to find the smallest expression that is divisible by both expressions.
Let's break down each expression:
4(xy)2 can be simplified as 4x2y2.
3(x)3y can be simplified as 3x3y.
To find the LCM, we need to find the highest power of each variable that appears in either expression. In this case, we have x to the power of 2 and x to the power of 3, so the highest power of x is x to the power of 3. Similarly, we have y to the power of 2 in the first expression, so the highest power of y is y to the power of 2.
Therefore, the LCM is (x3)(y2), which can be represented as (x cubed)(y squared) or (x^3)(y^2).
To find the least common multiple (LCM) of two expressions, we need to first factorize each expression into its prime factors. Then, we identify the common prime factors and take the highest power of each factor.
Let's factorize the given expressions:
Expression 1: 4(xy)^2 = 4(x^1y^1)^2 = 4*x^2*y^2 = 2^2 * x^2 * y^2
Expression 2: 3(x)^3y = 3 * (x^3) * y^1 = 3 * x^3 * y
To find the LCM, we take the highest power of each prime factor:
Prime factors: 2, 3, x, y
Highest powers:
2^2 * 3 * x^3 * y^2 = 12(x^3)(y^2)
Therefore, the least common multiple of the expressions 4(xy)^2 and 3(x)^3y is 12(x^3)(y^2).