GCD & LCM Calculator
Solve Greatest Common Divisor and Least Common Multiple for integers or fractions, with step-by-step arithmetic.
Number Type
Number Grid
Prime Factorization Breakdown
Number: 122² × 3
Number: 182 × 3²
Number: 242³ × 3
Step-by-Step Euclidean Algorithm (GCD of first two numbers)
18 = 12 × 1 + 6
12 = 6 × 2 + 0
The last non-zero remainder is 6. So, GCD = 6.
Greatest Common Divisor (GCD)
6
Least Common Multiple (LCM)
72
Fraction Rules: GCD of fractions equals GCD of numerators divided by LCM of denominators. LCM of fractions equals LCM of numerators divided by GCD of denominators.
GCD and LCM, explained with fractional methods
The greatest common divisor (GCD/HCF) identifies the largest positive integer dividing a set of values with zero remainders. The least common multiple (LCM) finds the smallest multiple shared by all values in a set.
Decimals and fractions can be solved by multiplying values to find base common factors, then scaling back the output divisors and multiples.
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