What is the Least Common Multiple of 30174 and 30189?

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 30174 and 30189 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30174 and 30189, than apply into the LCM equation.

GCF(30174,30189) = 3
LCM(30174,30189) = ( 30174 × 30189) / 3
LCM(30174,30189) = 910922886 / 3
LCM(30174,30189) = 303640962

Least Common Multiple (LCM) of 30174 and 30189 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30174 and 30189. First we will calculate the prime factors of 30174 and 30189.

Prime Factorization of 30174

Prime Factorization of 30189

Now multiplying the highest exponent prime factors to calculate the LCM of 30174 and 30189.

LCM(30174,30189) = 2¹ × 3¹ × 47¹ × 107¹ × 29¹ × 347¹
LCM(30174,30189) = 303640962