What is the Least Common Multiple of 12114 and 12129?

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 12114 and 12129 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12114 and 12129, than apply into the LCM equation.

GCF(12114,12129) = 3
LCM(12114,12129) = ( 12114 × 12129) / 3
LCM(12114,12129) = 146930706 / 3
LCM(12114,12129) = 48976902

Least Common Multiple (LCM) of 12114 and 12129 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12114 and 12129. First we will calculate the prime factors of 12114 and 12129.

Prime Factorization of 12114

Prime Factorization of 12129

Now multiplying the highest exponent prime factors to calculate the LCM of 12114 and 12129.

LCM(12114,12129) = 2¹ × 3² × 673¹ × 13¹ × 311¹
LCM(12114,12129) = 48976902