Final answer:
The prime factorization for lcm(x, y) is the product of the prime factors of x and y, raised to the highest power it appears in either x or y.
Step-by-step explanation:
The prime factorization for lcm(x, y) is the product of the prime factors of x and y, raised to the highest power it appears in either x or y. This means that you find the prime factorization for x and y separately, and then take the product of the highest power of each prime factor.
For example, if the prime factorization of x is 2^3 * 3^2 * 5 and the prime factorization of y is 2^2 * 3 * 7, then the prime factorization for lcm(x, y) would be 2^3 * 3^2 * 5 * 7, since the highest power of 2, 3, and 5 appear in x, while the highest power of 7 appears in y.