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\[ 126 = 2 \times 3^2 \times 7 \]The GCF is found by taking the lowest power of all common prime factors:Common primes: 2, 3, 7Lowest powers: \(2^1\), \(3^1\), \(7^1\)Thus, the GCF is:\[ 2^1 \times 3^1 \times 7^1 = 42 \]The greatest common factor is \(\boxed{42}\).A programmer is developing an AI application that requires processing data packets. If the application handles packets every 18 seconds and another system processes every 24 seconds, what is the least common multiple of these two processing times?To find the least common multiple (LCM) of 18 and 24, we first determine their prime factorizations:\[ 18 = 2 \times 3^2 \]