The common divisors of two numbers are the divisors they share, and the largest among them is called the greatest common divisor (GCD). For example, for the natural numbers and , the divisors are:

Thus, the common divisors of and are , , , and the GCD is .

If two natural numbers, such as and , have a GCD of , they are called relatively prime.

Using prime factorization, we can find the GCD as follows:
Prime factorize and and express them using exponents:

The GCD is determined by selecting the common prime factors and taking the lower exponent for each.

In general, the GCD of two or more natural numbers can be found by prime factorizing each number and following this method.

The common multiples of two numbers are the multiples they share, and the smallest among them is called the least common multiple (LCM). For example, the common multiples of and are , , , , and the LCM is .
All the common multiples of and are multiples of the LCM . In general, the common multiples of two or more natural numbers are all multiples of their LCM.

Using prime factorization, we can find the LCM as follows:
Prime factorize and and express them using exponents:

The LCM is determined by taking the highest exponent for each prime factor from the factorizations and multiplying them together.

In general, the LCM of two or more natural numbers can be found by prime factorizing each number and following this method.