What is the Least Common Multiple of 30900 and 30912?

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 30900 and 30912 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30900 and 30912, than apply into the LCM equation.

GCF(30900,30912) = 12
LCM(30900,30912) = ( 30900 × 30912) / 12
LCM(30900,30912) = 955180800 / 12
LCM(30900,30912) = 79598400

Least Common Multiple (LCM) of 30900 and 30912 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30900 and 30912. First we will calculate the prime factors of 30900 and 30912.

Prime Factorization of 30900

Prime Factorization of 30912

Now multiplying the highest exponent prime factors to calculate the LCM of 30900 and 30912.

LCM(30900,30912) = 2⁶ × 3¹ × 5² × 103¹ × 7¹ × 23¹
LCM(30900,30912) = 79598400