What is the Least Common Multiple of 55305 and 55314?

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 55305 and 55314 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 55305 and 55314, than apply into the LCM equation.

GCF(55305,55314) = 9
LCM(55305,55314) = ( 55305 × 55314) / 9
LCM(55305,55314) = 3059140770 / 9
LCM(55305,55314) = 339904530

Least Common Multiple (LCM) of 55305 and 55314 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 55305 and 55314. First we will calculate the prime factors of 55305 and 55314.

Prime Factorization of 55305

Prime Factorization of 55314

Now multiplying the highest exponent prime factors to calculate the LCM of 55305 and 55314.

LCM(55305,55314) = 3² × 5¹ × 1229¹ × 2¹ × 7¹ × 439¹
LCM(55305,55314) = 339904530