What is the Least Common Multiple of 1565 and 1584?

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 1565 and 1584 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1565 and 1584, than apply into the LCM equation.

GCF(1565,1584) = 1
LCM(1565,1584) = ( 1565 × 1584) / 1
LCM(1565,1584) = 2478960 / 1
LCM(1565,1584) = 2478960

Least Common Multiple (LCM) of 1565 and 1584 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1565 and 1584. First we will calculate the prime factors of 1565 and 1584.

Prime Factorization of 1565

Prime Factorization of 1584

Now multiplying the highest exponent prime factors to calculate the LCM of 1565 and 1584.

LCM(1565,1584) = 5¹ × 313¹ × 2⁴ × 3² × 11¹
LCM(1565,1584) = 2478960