What is the Least Common Multiple of 55200 and 55209?

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 55200 and 55209 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 55200 and 55209, than apply into the LCM equation.

GCF(55200,55209) = 3
LCM(55200,55209) = ( 55200 × 55209) / 3
LCM(55200,55209) = 3047536800 / 3
LCM(55200,55209) = 1015845600

Least Common Multiple (LCM) of 55200 and 55209 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 55200 and 55209. First we will calculate the prime factors of 55200 and 55209.

Prime Factorization of 55200

Prime Factorization of 55209

Now multiplying the highest exponent prime factors to calculate the LCM of 55200 and 55209.

LCM(55200,55209) = 2⁵ × 3¹ × 5² × 23¹ × 7¹ × 11¹ × 239¹
LCM(55200,55209) = 1015845600