What is the Least Common Multiple of 13824 and 13828?

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 13824 and 13828 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13824 and 13828, than apply into the LCM equation.

GCF(13824,13828) = 4
LCM(13824,13828) = ( 13824 × 13828) / 4
LCM(13824,13828) = 191158272 / 4
LCM(13824,13828) = 47789568

Least Common Multiple (LCM) of 13824 and 13828 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13824 and 13828. First we will calculate the prime factors of 13824 and 13828.

Prime Factorization of 13824

Prime Factorization of 13828

Now multiplying the highest exponent prime factors to calculate the LCM of 13824 and 13828.

LCM(13824,13828) = 2⁹ × 3³ × 3457¹
LCM(13824,13828) = 47789568