The GCD of 12 and 18 is 6, and their LCM is 36. Surprisingly, 6×36=216, and 12×18 is also exactly 216! This is not a coincidence—it is a relationship that always holds. Change the two numbers with the sliders and check whether this relationship always works.
Why does this relationship always hold? When you prime-factorize two numbers, the GCD collects the "common prime factors with the lower exponents," while the LCM collects "each prime factor with the higher exponents." When you multiply the prime factorizations of A and B, the result is exactly the same as combining the common part (what the GCD contains) with the remaining parts (what is additionally included in the LCM).
Once you know this relationship, you can quickly calculate the LCM when it is difficult to find directly: use "A×B÷GCD." If you find the GCD using the Euclidean algorithm, the LCM can be obtained immediately with just one division.