What is the Least Common Multiple of 19296 and 19312?

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 19296 and 19312 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19296 and 19312, than apply into the LCM equation.

GCF(19296,19312) = 16
LCM(19296,19312) = ( 19296 × 19312) / 16
LCM(19296,19312) = 372644352 / 16
LCM(19296,19312) = 23290272

Least Common Multiple (LCM) of 19296 and 19312 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19296 and 19312. First we will calculate the prime factors of 19296 and 19312.

Prime Factorization of 19296

Prime Factorization of 19312

Now multiplying the highest exponent prime factors to calculate the LCM of 19296 and 19312.

LCM(19296,19312) = 2⁵ × 3² × 67¹ × 17¹ × 71¹
LCM(19296,19312) = 23290272