What is the Least Common Multiple of 72084 and 72096?

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 72084 and 72096 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 72084 and 72096, than apply into the LCM equation.

GCF(72084,72096) = 12
LCM(72084,72096) = ( 72084 × 72096) / 12
LCM(72084,72096) = 5196968064 / 12
LCM(72084,72096) = 433080672

Least Common Multiple (LCM) of 72084 and 72096 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 72084 and 72096. First we will calculate the prime factors of 72084 and 72096.

Prime Factorization of 72084

Prime Factorization of 72096

Now multiplying the highest exponent prime factors to calculate the LCM of 72084 and 72096.

LCM(72084,72096) = 2⁵ × 3¹ × 6007¹ × 751¹
LCM(72084,72096) = 433080672