What is the Least Common Multiple of 90585 and 90600?

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 90585 and 90600 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 90585 and 90600, than apply into the LCM equation.

GCF(90585,90600) = 15
LCM(90585,90600) = ( 90585 × 90600) / 15
LCM(90585,90600) = 8207001000 / 15
LCM(90585,90600) = 547133400

Least Common Multiple (LCM) of 90585 and 90600 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 90585 and 90600. First we will calculate the prime factors of 90585 and 90600.

Prime Factorization of 90585

Prime Factorization of 90600

Now multiplying the highest exponent prime factors to calculate the LCM of 90585 and 90600.

LCM(90585,90600) = 3³ × 5² × 11¹ × 61¹ × 2³ × 151¹
LCM(90585,90600) = 547133400