What is the Least Common Multiple of 30804 and 30816?

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 30804 and 30816 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30804 and 30816, than apply into the LCM equation.

GCF(30804,30816) = 12
LCM(30804,30816) = ( 30804 × 30816) / 12
LCM(30804,30816) = 949256064 / 12
LCM(30804,30816) = 79104672

Least Common Multiple (LCM) of 30804 and 30816 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30804 and 30816. First we will calculate the prime factors of 30804 and 30816.

Prime Factorization of 30804

Prime Factorization of 30816

Now multiplying the highest exponent prime factors to calculate the LCM of 30804 and 30816.

LCM(30804,30816) = 2⁵ × 3² × 17¹ × 151¹ × 107¹
LCM(30804,30816) = 79104672