Is the LCM for xy, y3 = x3y3, y3

To find the least common multiple (LCM) of two or more numbers, we need to identify the common factors and the highest power of each factor.

In this case, we are finding the LCM of the numbers xy and y^3, which can be represented as x * y and y * y * y, respectively.

To determine the LCM, we need to identify the highest power of each factor. In this case, we have:

x * y --> The highest power of x is x^1, and the highest power of y is y^1.
y^3 --> We already have y^1, but we need to consider the highest power which is y^3.

To calculate the LCM, we multiply the factors with their highest powers:

LCM = x^1 * y^3 = x * y^3

Thus, the LCM for xy, y^3 = xy^3.

To find the least common multiple (LCM) of two numbers or expressions, we need to determine the highest power of each factor appearing in either of them. Let's break down the given expressions:

Expression 1: xy
Factors: x and y

Expression 2: x^3y^3
Factors: x (appears with a power of 3) and y (appears with a power of 3)

Now, let's compare the factors in both expressions:

- The factor x appears with a power of 1 in xy, and with a power of 3 in x^3y^3. The higher power of x is 3.
- The factor y appears with a power of 1 in xy, and with a power of 3 in x^3y^3. The higher power of y is 3.

Therefore, the LCM of xy and x^3y^3 is x^3y^3 since it contains the highest power of each factor.