What is the Least Common Multiple of 19664 and 19680?

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 19664 and 19680 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19664 and 19680, than apply into the LCM equation.

GCF(19664,19680) = 16
LCM(19664,19680) = ( 19664 × 19680) / 16
LCM(19664,19680) = 386987520 / 16
LCM(19664,19680) = 24186720

Least Common Multiple (LCM) of 19664 and 19680 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19664 and 19680. First we will calculate the prime factors of 19664 and 19680.

Prime Factorization of 19664

Prime Factorization of 19680

Now multiplying the highest exponent prime factors to calculate the LCM of 19664 and 19680.

LCM(19664,19680) = 2⁵ × 1229¹ × 3¹ × 5¹ × 41¹
LCM(19664,19680) = 24186720