What is the Least Common Multiple of 30012 and 30024?

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 30024 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 30024, than apply into the LCM equation.

GCF(30012,30024) = 12
LCM(30012,30024) = ( 30012 × 30024) / 12
LCM(30012,30024) = 901080288 / 12
LCM(30012,30024) = 75090024

Least Common Multiple (LCM) of 30012 and 30024 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30012 and 30024. First we will calculate the prime factors of 30012 and 30024.

Prime Factorization of 30012

Prime Factorization of 30024

Now multiplying the highest exponent prime factors to calculate the LCM of 30012 and 30024.

LCM(30012,30024) = 2³ × 3³ × 41¹ × 61¹ × 139¹
LCM(30012,30024) = 75090024