What is the Least Common Multiple of 19680 and 19696?

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 19680 and 19696 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19680 and 19696, than apply into the LCM equation.

GCF(19680,19696) = 16
LCM(19680,19696) = ( 19680 × 19696) / 16
LCM(19680,19696) = 387617280 / 16
LCM(19680,19696) = 24226080

Least Common Multiple (LCM) of 19680 and 19696 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19680 and 19696. First we will calculate the prime factors of 19680 and 19696.

Prime Factorization of 19680

Prime Factorization of 19696

Now multiplying the highest exponent prime factors to calculate the LCM of 19680 and 19696.

LCM(19680,19696) = 2⁵ × 3¹ × 5¹ × 41¹ × 1231¹
LCM(19680,19696) = 24226080