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Alright, darling, let's get down to business. First, we break down each number into its prime factors: 6 = 2 x 3, 24 = 2^3 x 3, and 32 = 2^5. Then, we take the highest power of each prime factor that appears in any of the numbers: 2^5 x 3 = 96. So, the LCM of 6, 24, and 32 using prime factorization is 96. Hope that clears things up for you, sugar!
lcm(6, 24, 32) = 96.
6 = 2 x 3
24 = 2^3 x 3
32 = 2^5
lcm = 2^5 x 3 = 96
Each number is represented in its prime factorization in power format. The LCM is then calculated as the product of each prime to its highest power across all the factorizations.
2 x 3 = 6
2 x 2 x 2 x 3 = 24
2 x 2 x 2 x 2 x 2 = 32
2 x 2 x 2 x 2 x 2 x 3 = 96, the LCM
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