What is the Least Common Multiple of 19092 and 19104?

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 19092 and 19104 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19092 and 19104, than apply into the LCM equation.

GCF(19092,19104) = 12
LCM(19092,19104) = ( 19092 × 19104) / 12
LCM(19092,19104) = 364733568 / 12
LCM(19092,19104) = 30394464

Least Common Multiple (LCM) of 19092 and 19104 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19092 and 19104. First we will calculate the prime factors of 19092 and 19104.

Prime Factorization of 19092

Prime Factorization of 19104

Now multiplying the highest exponent prime factors to calculate the LCM of 19092 and 19104.

LCM(19092,19104) = 2⁵ × 3¹ × 37¹ × 43¹ × 199¹
LCM(19092,19104) = 30394464