What is the Least Common Multiple of 58209 and 58224?

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 58209 and 58224 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 58209 and 58224, than apply into the LCM equation.

GCF(58209,58224) = 3
LCM(58209,58224) = ( 58209 × 58224) / 3
LCM(58209,58224) = 3389160816 / 3
LCM(58209,58224) = 1129720272

Least Common Multiple (LCM) of 58209 and 58224 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 58209 and 58224. First we will calculate the prime factors of 58209 and 58224.

Prime Factorization of 58209

Prime Factorization of 58224

Now multiplying the highest exponent prime factors to calculate the LCM of 58209 and 58224.

LCM(58209,58224) = 3¹ × 19403¹ × 2⁴ × 1213¹
LCM(58209,58224) = 1129720272