What is the Least Common Multiple of 12006 and 12014?

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 12006 and 12014 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12006 and 12014, than apply into the LCM equation.

GCF(12006,12014) = 2
LCM(12006,12014) = ( 12006 × 12014) / 2
LCM(12006,12014) = 144240084 / 2
LCM(12006,12014) = 72120042

Least Common Multiple (LCM) of 12006 and 12014 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12006 and 12014. First we will calculate the prime factors of 12006 and 12014.

Prime Factorization of 12006

Prime Factorization of 12014

Now multiplying the highest exponent prime factors to calculate the LCM of 12006 and 12014.

LCM(12006,12014) = 2¹ × 3² × 23¹ × 29¹ × 6007¹
LCM(12006,12014) = 72120042