What is the Least Common Multiple of 12192 and 12205?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least Common Multiple of 12192 and 12205 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12192 and 12205, than apply into the LCM equation.

GCF(12192,12205) = 1
LCM(12192,12205) = ( 12192 × 12205) / 1
LCM(12192,12205) = 148803360 / 1
LCM(12192,12205) = 148803360

Least Common Multiple (LCM) of 12192 and 12205 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12192 and 12205. First we will calculate the prime factors of 12192 and 12205.

Prime Factorization of 12192

Prime Factorization of 12205

Now multiplying the highest exponent prime factors to calculate the LCM of 12192 and 12205.

LCM(12192,12205) = 2⁵ × 3¹ × 127¹ × 5¹ × 2441¹
LCM(12192,12205) = 148803360