What is the Least Common Multiple of 75312 and 75332?

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 75312 and 75332 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75312 and 75332, than apply into the LCM equation.

GCF(75312,75332) = 4
LCM(75312,75332) = ( 75312 × 75332) / 4
LCM(75312,75332) = 5673403584 / 4
LCM(75312,75332) = 1418350896

Least Common Multiple (LCM) of 75312 and 75332 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75312 and 75332. First we will calculate the prime factors of 75312 and 75332.

Prime Factorization of 75312

Prime Factorization of 75332

Now multiplying the highest exponent prime factors to calculate the LCM of 75312 and 75332.

LCM(75312,75332) = 2⁴ × 3² × 523¹ × 37¹ × 509¹
LCM(75312,75332) = 1418350896