What is the Least Common Multiple of 30006 and 30021?

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 30006 and 30021 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30006 and 30021, than apply into the LCM equation.

GCF(30006,30021) = 3
LCM(30006,30021) = ( 30006 × 30021) / 3
LCM(30006,30021) = 900810126 / 3
LCM(30006,30021) = 300270042

Least Common Multiple (LCM) of 30006 and 30021 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30006 and 30021. First we will calculate the prime factors of 30006 and 30021.

Prime Factorization of 30006

Prime Factorization of 30021

Now multiplying the highest exponent prime factors to calculate the LCM of 30006 and 30021.

LCM(30006,30021) = 2¹ × 3² × 1667¹ × 10007¹
LCM(30006,30021) = 300270042