What is the Least Common Multiple of 13872 and 13889?

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 13872 and 13889 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13872 and 13889, than apply into the LCM equation.

GCF(13872,13889) = 17
LCM(13872,13889) = ( 13872 × 13889) / 17
LCM(13872,13889) = 192668208 / 17
LCM(13872,13889) = 11333424

Least Common Multiple (LCM) of 13872 and 13889 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13872 and 13889. First we will calculate the prime factors of 13872 and 13889.

Prime Factorization of 13872

Prime Factorization of 13889

Now multiplying the highest exponent prime factors to calculate the LCM of 13872 and 13889.

LCM(13872,13889) = 2⁴ × 3¹ × 17² × 19¹ × 43¹
LCM(13872,13889) = 11333424