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Finding least common multiples is a primary application of prime factorization because it involves breaking down numbers into their prime factors to identify the smallest common multiple. To find the least common multiple (LCM) of two or more numbers, you first factor each number into its prime components.

Once the prime factorization is obtained, the LCM is determined by taking the highest power of each prime factor that appears in the factorizations. This method ensures that the LCM will be the smallest multiple that is evenly divisible by all the numbers involved. Prime factorization simplifies the process of identifying these prime factors, making it easier to compute the LCM efficiently.

In contrast, solving algebraic equations, determining averages, and calculating median values do not rely directly on prime factorization techniques. These processes engage different mathematical principles and methods that are unrelated to the breakdown of integers into prime components.