What is the Least Common Multiple of 565 and 585?

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 565 and 585 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 565 and 585, than apply into the LCM equation.

GCF(565,585) = 5
LCM(565,585) = ( 565 × 585) / 5
LCM(565,585) = 330525 / 5
LCM(565,585) = 66105

Least Common Multiple (LCM) of 565 and 585 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 565 and 585. First we will calculate the prime factors of 565 and 585.

Prime Factorization of 565

Prime Factorization of 585

Now multiplying the highest exponent prime factors to calculate the LCM of 565 and 585.

LCM(565,585) = 5¹ × 113¹ × 3² × 13¹
LCM(565,585) = 66105