What is the Least Common Multiple of 30168 and 30174?

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 30168 and 30174 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30168 and 30174, than apply into the LCM equation.

GCF(30168,30174) = 6
LCM(30168,30174) = ( 30168 × 30174) / 6
LCM(30168,30174) = 910289232 / 6
LCM(30168,30174) = 151714872

Least Common Multiple (LCM) of 30168 and 30174 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30168 and 30174. First we will calculate the prime factors of 30168 and 30174.

Prime Factorization of 30168

Prime Factorization of 30174

Now multiplying the highest exponent prime factors to calculate the LCM of 30168 and 30174.

LCM(30168,30174) = 2³ × 3² × 419¹ × 47¹ × 107¹
LCM(30168,30174) = 151714872