What is the Least Common Multiple of 19404 and 19416?

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 19404 and 19416 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19404 and 19416, than apply into the LCM equation.

GCF(19404,19416) = 12
LCM(19404,19416) = ( 19404 × 19416) / 12
LCM(19404,19416) = 376748064 / 12
LCM(19404,19416) = 31395672

Least Common Multiple (LCM) of 19404 and 19416 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19404 and 19416. First we will calculate the prime factors of 19404 and 19416.

Prime Factorization of 19404

Prime Factorization of 19416

Now multiplying the highest exponent prime factors to calculate the LCM of 19404 and 19416.

LCM(19404,19416) = 2³ × 3² × 7² × 11¹ × 809¹
LCM(19404,19416) = 31395672