What is the Least Common Multiple of 75204 and 75214?

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 75204 and 75214 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75204 and 75214, than apply into the LCM equation.

GCF(75204,75214) = 2
LCM(75204,75214) = ( 75204 × 75214) / 2
LCM(75204,75214) = 5656393656 / 2
LCM(75204,75214) = 2828196828

Least Common Multiple (LCM) of 75204 and 75214 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75204 and 75214. First we will calculate the prime factors of 75204 and 75214.

Prime Factorization of 75204

Prime Factorization of 75214

Now multiplying the highest exponent prime factors to calculate the LCM of 75204 and 75214.

LCM(75204,75214) = 2² × 3² × 2089¹ × 37607¹
LCM(75204,75214) = 2828196828