What is the Least Common Multiple of 12096 and 12114?

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 12096 and 12114 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12096 and 12114, than apply into the LCM equation.

GCF(12096,12114) = 18
LCM(12096,12114) = ( 12096 × 12114) / 18
LCM(12096,12114) = 146530944 / 18
LCM(12096,12114) = 8140608

Least Common Multiple (LCM) of 12096 and 12114 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12096 and 12114. First we will calculate the prime factors of 12096 and 12114.

Prime Factorization of 12096

Prime Factorization of 12114

Now multiplying the highest exponent prime factors to calculate the LCM of 12096 and 12114.

LCM(12096,12114) = 2⁶ × 3³ × 7¹ × 673¹
LCM(12096,12114) = 8140608