What is the Least Common Multiple of 12105 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 12105 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 12105 and 12114, than apply into the LCM equation.

GCF(12105,12114) = 9
LCM(12105,12114) = ( 12105 × 12114) / 9
LCM(12105,12114) = 146639970 / 9
LCM(12105,12114) = 16293330

Least Common Multiple (LCM) of 12105 and 12114 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12105 and 12114. First we will calculate the prime factors of 12105 and 12114.

Prime Factorization of 12105

Prime Factorization of 12114

Now multiplying the highest exponent prime factors to calculate the LCM of 12105 and 12114.

LCM(12105,12114) = 3² × 5¹ × 269¹ × 2¹ × 673¹
LCM(12105,12114) = 16293330