What is the Least Common Multiple of 30024 and 30038?

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 30024 and 30038 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30024 and 30038, than apply into the LCM equation.

GCF(30024,30038) = 2
LCM(30024,30038) = ( 30024 × 30038) / 2
LCM(30024,30038) = 901860912 / 2
LCM(30024,30038) = 450930456

Least Common Multiple (LCM) of 30024 and 30038 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30024 and 30038. First we will calculate the prime factors of 30024 and 30038.

Prime Factorization of 30024

Prime Factorization of 30038

Now multiplying the highest exponent prime factors to calculate the LCM of 30024 and 30038.

LCM(30024,30038) = 2³ × 3³ × 139¹ × 23¹ × 653¹
LCM(30024,30038) = 450930456