What is the Least Common Multiple of 72008 and 72024?

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 72008 and 72024 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 72008 and 72024, than apply into the LCM equation.

GCF(72008,72024) = 8
LCM(72008,72024) = ( 72008 × 72024) / 8
LCM(72008,72024) = 5186304192 / 8
LCM(72008,72024) = 648288024

Least Common Multiple (LCM) of 72008 and 72024 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 72008 and 72024. First we will calculate the prime factors of 72008 and 72024.

Prime Factorization of 72008

Prime Factorization of 72024

Now multiplying the highest exponent prime factors to calculate the LCM of 72008 and 72024.

LCM(72008,72024) = 2³ × 9001¹ × 3¹ × 3001¹
LCM(72008,72024) = 648288024