What is the Least Common Multiple of 54585 and 54600?

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 54585 and 54600 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54585 and 54600, than apply into the LCM equation.

GCF(54585,54600) = 15
LCM(54585,54600) = ( 54585 × 54600) / 15
LCM(54585,54600) = 2980341000 / 15
LCM(54585,54600) = 198689400

Least Common Multiple (LCM) of 54585 and 54600 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54585 and 54600. First we will calculate the prime factors of 54585 and 54600.

Prime Factorization of 54585

Prime Factorization of 54600

Now multiplying the highest exponent prime factors to calculate the LCM of 54585 and 54600.

LCM(54585,54600) = 3² × 5² × 1213¹ × 2³ × 7¹ × 13¹
LCM(54585,54600) = 198689400