What is the Least Common Multiple of 19696 and 19704?

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 19696 and 19704 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19696 and 19704, than apply into the LCM equation.

GCF(19696,19704) = 8
LCM(19696,19704) = ( 19696 × 19704) / 8
LCM(19696,19704) = 388089984 / 8
LCM(19696,19704) = 48511248

Least Common Multiple (LCM) of 19696 and 19704 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19696 and 19704. First we will calculate the prime factors of 19696 and 19704.

Prime Factorization of 19696

Prime Factorization of 19704

Now multiplying the highest exponent prime factors to calculate the LCM of 19696 and 19704.

LCM(19696,19704) = 2⁴ × 1231¹ × 3¹ × 821¹
LCM(19696,19704) = 48511248