What is the Least Common Multiple of 2565 and 2584?

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 2565 and 2584 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2565 and 2584, than apply into the LCM equation.

GCF(2565,2584) = 19
LCM(2565,2584) = ( 2565 × 2584) / 19
LCM(2565,2584) = 6627960 / 19
LCM(2565,2584) = 348840

Least Common Multiple (LCM) of 2565 and 2584 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2565 and 2584. First we will calculate the prime factors of 2565 and 2584.

Prime Factorization of 2565

Prime Factorization of 2584

Now multiplying the highest exponent prime factors to calculate the LCM of 2565 and 2584.

LCM(2565,2584) = 3³ × 5¹ × 19¹ × 2³ × 17¹
LCM(2565,2584) = 348840