What is the Least Common Multiple of 19504 and 19512?

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 19504 and 19512 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19504 and 19512, than apply into the LCM equation.

GCF(19504,19512) = 8
LCM(19504,19512) = ( 19504 × 19512) / 8
LCM(19504,19512) = 380562048 / 8
LCM(19504,19512) = 47570256

Least Common Multiple (LCM) of 19504 and 19512 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19504 and 19512. First we will calculate the prime factors of 19504 and 19512.

Prime Factorization of 19504

Prime Factorization of 19512

Now multiplying the highest exponent prime factors to calculate the LCM of 19504 and 19512.

LCM(19504,19512) = 2⁴ × 23¹ × 53¹ × 3² × 271¹
LCM(19504,19512) = 47570256