What is the Least Common Multiple of 75300 and 75312?

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 75300 and 75312 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75300 and 75312, than apply into the LCM equation.

GCF(75300,75312) = 12
LCM(75300,75312) = ( 75300 × 75312) / 12
LCM(75300,75312) = 5670993600 / 12
LCM(75300,75312) = 472582800

Least Common Multiple (LCM) of 75300 and 75312 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75300 and 75312. First we will calculate the prime factors of 75300 and 75312.

Prime Factorization of 75300

Prime Factorization of 75312

Now multiplying the highest exponent prime factors to calculate the LCM of 75300 and 75312.

LCM(75300,75312) = 2⁴ × 3² × 5² × 251¹ × 523¹
LCM(75300,75312) = 472582800