GCF Gcd Calculator
gcf/gcd calculator. Get instant, accurate results. Enter values for instant results with step-by-step formulas.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
GCD(a,b) = GCD(b, a mod b) | LCM = a×b / GCD(a,b)
The Euclidean algorithm repeatedly replaces the larger number with the remainder of dividing it by the smaller number until the remainder reaches zero — the last nonzero remainder is the GCD. Once the GCD is known, the LCM follows directly from the identity GCD(a,b) × LCM(a,b) = a × b.
Worked Examples
Example 1: 48 and 36
Problem:GCD(48, 36)
Solution:48 = 2⁴×3, 36 = 2²×3². GCD = 2²×3 = 12. LCM = 48×36/12 = 144
Result:GCD=12, LCM=144
Example 2: Coprime numbers: 17 and 25
Problem:GCD(17, 25)
Solution:17 is prime and does not divide 25, so their only common factor is 1. GCD = 1. LCM = 17×25/1 = 425.
Result:GCD=1 (coprime), LCM=425
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy