Greatest common divisor
Using prime factorizations

Greatest common divisors can be computed by determining the prime factorizations of the two numbers and comparing factors. For example, to compute gcd(48, 180), we find the prime factorizations 48 = 2 · 3 and 180 = 2 · 3 · 5; the GCD is then 2 · 3 · 5 = 2 · 3 · 5 = 12 The corresponding LCM is then2 · 3 · 5 = 2 · 3 · 5 = 720.

In practice, this method is only feasible for small numbers, as computing prime factorizations takes too long.
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