Find the product of the greatest common divisor and the least common multiple of $18$ and $42.$
One way to find the GCD and the LCM is to use prime factorization. I can write $18$ and $42$ as products of prime factors: $18 = 2 \times 3 \times 3$ and $42 = 2 \times 3 \times 7.$ To find the GCD, I need to find the common prime factors with the lowest powers: $GCD(18,42) = 2 \times 3 = 6.$ To find the LCM, I need to find the prime factors with the highest powers: $LCM(18,42) = 2 \times 3 \times 3 \times 7 = 126.$ Now I have the GCD and the LCM, and I can find their product: $GCD(18,42) \times LCM(18,42) = 6 \times 126 = 756.$ 