What is the Least Common Multiple of 27009 and 27024?

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 27009 and 27024 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 27009 and 27024, than apply into the LCM equation.

GCF(27009,27024) = 3
LCM(27009,27024) = ( 27009 × 27024) / 3
LCM(27009,27024) = 729891216 / 3
LCM(27009,27024) = 243297072

Least Common Multiple (LCM) of 27009 and 27024 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 27009 and 27024. First we will calculate the prime factors of 27009 and 27024.

Prime Factorization of 27009

Prime Factorization of 27024

Now multiplying the highest exponent prime factors to calculate the LCM of 27009 and 27024.

LCM(27009,27024) = 3² × 3001¹ × 2⁴ × 563¹
LCM(27009,27024) = 243297072