What is the Least Common Multiple of 30084 and 30096?

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 30096 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 30096, than apply into the LCM equation.

GCF(30084,30096) = 12
LCM(30084,30096) = ( 30084 × 30096) / 12
LCM(30084,30096) = 905408064 / 12
LCM(30084,30096) = 75450672

Least Common Multiple (LCM) of 30084 and 30096 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30084 and 30096. First we will calculate the prime factors of 30084 and 30096.

Prime Factorization of 30084

Prime Factorization of 30096

Now multiplying the highest exponent prime factors to calculate the LCM of 30084 and 30096.

LCM(30084,30096) = 2⁴ × 3² × 23¹ × 109¹ × 11¹ × 19¹
LCM(30084,30096) = 75450672