What is the Least Common Multiple of 13804 and 13824?

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 13804 and 13824 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13804 and 13824, than apply into the LCM equation.

GCF(13804,13824) = 4
LCM(13804,13824) = ( 13804 × 13824) / 4
LCM(13804,13824) = 190826496 / 4
LCM(13804,13824) = 47706624

Least Common Multiple (LCM) of 13804 and 13824 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13804 and 13824. First we will calculate the prime factors of 13804 and 13824.

Prime Factorization of 13804

Prime Factorization of 13824

Now multiplying the highest exponent prime factors to calculate the LCM of 13804 and 13824.

LCM(13804,13824) = 2⁹ × 7¹ × 17¹ × 29¹ × 3³
LCM(13804,13824) = 47706624