What is the Least Common Multiple of 30012 and 30016?

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 30012 and 30016 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30012 and 30016, than apply into the LCM equation.

GCF(30012,30016) = 4
LCM(30012,30016) = ( 30012 × 30016) / 4
LCM(30012,30016) = 900840192 / 4
LCM(30012,30016) = 225210048

Least Common Multiple (LCM) of 30012 and 30016 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30012 and 30016. First we will calculate the prime factors of 30012 and 30016.

Prime Factorization of 30012

Prime Factorization of 30016

Now multiplying the highest exponent prime factors to calculate the LCM of 30012 and 30016.

LCM(30012,30016) = 2⁶ × 3¹ × 41¹ × 61¹ × 7¹ × 67¹
LCM(30012,30016) = 225210048