What is the Least Common Multiple of 30024 and 30039?

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 30039 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 30039, than apply into the LCM equation.

GCF(30024,30039) = 3
LCM(30024,30039) = ( 30024 × 30039) / 3
LCM(30024,30039) = 901890936 / 3
LCM(30024,30039) = 300630312

Least Common Multiple (LCM) of 30024 and 30039 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30024 and 30039. First we will calculate the prime factors of 30024 and 30039.

Prime Factorization of 30024

Prime Factorization of 30039

Now multiplying the highest exponent prime factors to calculate the LCM of 30024 and 30039.

LCM(30024,30039) = 2³ × 3³ × 139¹ × 17¹ × 19¹ × 31¹
LCM(30024,30039) = 300630312