Two positive integers a and b can be written as a = x3y2 and b = xy3. x, y are prime numbers

Introduction:
We are given two positive integers a and b which can be written in a certain form. We need to find the LCM (Least Common Multiple) of a and b.

Given Information:
- a = x(cube) * y(square)
- b = XY(cube)
- x, y, X, and Y are integers

Approach:
To find the LCM of a and b, we need to find the highest power of each prime factor that appears in either a or b.

Prime Factorization of a:
The prime factorization of a can be written as:
a = x(cube) * y(square)

The prime factors of a are:
- x (appears three times)
- y (appears two times)

Prime Factorization of b:
The prime factorization of b can be written as:
b = XY(cube)

The prime factors of b are:
- X (appears three times)
- Y (appears one time)

Finding the LCM:
To find the LCM, we need to consider the highest power of each prime factor that appears in either a or b.

The LCM of a and b will be:
LCM(a, b) = (x^3) * (y^2) * (X^3) * Y

Example:
Let's consider an example:
a = 2^3 * 3^2 = 8 * 9 = 72
b = 5^3 * 7 = 125 * 7 = 875

The LCM of a and b will be:
LCM(a, b) = (2^3) * (3^2) * (5^3) * 7 = 8 * 9 * 125 * 7 = 63000

Conclusion:
The LCM of the given positive integers a and b, which can be written as a = x(cube) * y(square) and b = XY(cube), is (x^3) * (y^2) * (X^3) * Y.