What is the Least Common Multiple of 30066 and 30075?

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 30066 and 30075 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30066 and 30075, than apply into the LCM equation.

GCF(30066,30075) = 3
LCM(30066,30075) = ( 30066 × 30075) / 3
LCM(30066,30075) = 904234950 / 3
LCM(30066,30075) = 301411650

Least Common Multiple (LCM) of 30066 and 30075 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30066 and 30075. First we will calculate the prime factors of 30066 and 30075.

Prime Factorization of 30066

Prime Factorization of 30075

Now multiplying the highest exponent prime factors to calculate the LCM of 30066 and 30075.

LCM(30066,30075) = 2¹ × 3¹ × 5011¹ × 5² × 401¹
LCM(30066,30075) = 301411650