What is the Least Common Multiple of 30096 and 30112?

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 30096 and 30112 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30096 and 30112, than apply into the LCM equation.

GCF(30096,30112) = 16
LCM(30096,30112) = ( 30096 × 30112) / 16
LCM(30096,30112) = 906250752 / 16
LCM(30096,30112) = 56640672

Least Common Multiple (LCM) of 30096 and 30112 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30096 and 30112. First we will calculate the prime factors of 30096 and 30112.

Prime Factorization of 30096

Prime Factorization of 30112

Now multiplying the highest exponent prime factors to calculate the LCM of 30096 and 30112.

LCM(30096,30112) = 2⁵ × 3² × 11¹ × 19¹ × 941¹
LCM(30096,30112) = 56640672