What is the Least Common Multiple of 30084 and 30093?

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 30084 and 30093 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30084 and 30093, than apply into the LCM equation.

GCF(30084,30093) = 3
LCM(30084,30093) = ( 30084 × 30093) / 3
LCM(30084,30093) = 905317812 / 3
LCM(30084,30093) = 301772604

Least Common Multiple (LCM) of 30084 and 30093 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30084 and 30093. First we will calculate the prime factors of 30084 and 30093.

Prime Factorization of 30084

Prime Factorization of 30093

Now multiplying the highest exponent prime factors to calculate the LCM of 30084 and 30093.

LCM(30084,30093) = 2² × 3¹ × 23¹ × 109¹ × 7¹ × 1433¹
LCM(30084,30093) = 301772604