Coprime Integers
Definition
A pair of integers \(a\) and \(b\) are called coprime or relatively prime if
\[ \mathrm{gcd}(a, b) = 1.\]
Theorem
A pair of integers \(a\) and \(b\) are coprime if and only if:
\[ \mathrm{lcm}(a, b) = ab.\]
This follows directly from the relationship between the greatest common denominator and lowest common multiple.