What is the formula to find the least common multiple of two numbers?

The least common multiple (LCM) of two numbers is found using the relationship between the LCM and the greatest common factor (GCF), also known as the greatest common divisor (GCD). The formula expresses that the product of the two numbers is equal to the product of their LCM and GCF.

Thus, to find the LCM, one can take the product of the two numbers and divide that product by their GCF. This method effectively helps to avoid counting the common multiples multiple times, ensuring that the resulting least common multiple is the smallest common multiple that both numbers share.

This approach is logical because the GCF represents how many times the common factors of the two numbers can fit into their product, isolating the multiples that are unique to each number and will give the smallest common multiple.