What is the Least Common Multiple of 19128 and 19140?

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 19128 and 19140 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19128 and 19140, than apply into the LCM equation.

GCF(19128,19140) = 12
LCM(19128,19140) = ( 19128 × 19140) / 12
LCM(19128,19140) = 366109920 / 12
LCM(19128,19140) = 30509160

Least Common Multiple (LCM) of 19128 and 19140 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19128 and 19140. First we will calculate the prime factors of 19128 and 19140.

Prime Factorization of 19128

Prime Factorization of 19140

Now multiplying the highest exponent prime factors to calculate the LCM of 19128 and 19140.

LCM(19128,19140) = 2³ × 3¹ × 797¹ × 5¹ × 11¹ × 29¹
LCM(19128,19140) = 30509160