What is the Least Common Multiple of 12054 and 12072?

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 12054 and 12072 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12054 and 12072, than apply into the LCM equation.

GCF(12054,12072) = 6
LCM(12054,12072) = ( 12054 × 12072) / 6
LCM(12054,12072) = 145515888 / 6
LCM(12054,12072) = 24252648

Least Common Multiple (LCM) of 12054 and 12072 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12054 and 12072. First we will calculate the prime factors of 12054 and 12072.

Prime Factorization of 12054

Prime Factorization of 12072

Now multiplying the highest exponent prime factors to calculate the LCM of 12054 and 12072.

LCM(12054,12072) = 2³ × 3¹ × 7² × 41¹ × 503¹
LCM(12054,12072) = 24252648