What is the Least Common Multiple of 585 and 590?

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 585 and 590 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 585 and 590, than apply into the LCM equation.

GCF(585,590) = 5
LCM(585,590) = ( 585 × 590) / 5
LCM(585,590) = 345150 / 5
LCM(585,590) = 69030

Least Common Multiple (LCM) of 585 and 590 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 585 and 590. First we will calculate the prime factors of 585 and 590.

Prime Factorization of 585

Prime Factorization of 590

Now multiplying the highest exponent prime factors to calculate the LCM of 585 and 590.

LCM(585,590) = 3² × 5¹ × 13¹ × 2¹ × 59¹
LCM(585,590) = 69030