What is the Least Common Multiple of 4575 and 4584?

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 4575 and 4584 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 4575 and 4584, than apply into the LCM equation.

GCF(4575,4584) = 3
LCM(4575,4584) = ( 4575 × 4584) / 3
LCM(4575,4584) = 20971800 / 3
LCM(4575,4584) = 6990600

Least Common Multiple (LCM) of 4575 and 4584 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 4575 and 4584. First we will calculate the prime factors of 4575 and 4584.

Prime Factorization of 4575

Prime Factorization of 4584

Now multiplying the highest exponent prime factors to calculate the LCM of 4575 and 4584.

LCM(4575,4584) = 3¹ × 5² × 61¹ × 2³ × 191¹
LCM(4575,4584) = 6990600