What is the Least Common Multiple of 75054 and 75072?

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 75054 and 75072 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75054 and 75072, than apply into the LCM equation.

GCF(75054,75072) = 6
LCM(75054,75072) = ( 75054 × 75072) / 6
LCM(75054,75072) = 5634453888 / 6
LCM(75054,75072) = 939075648

Least Common Multiple (LCM) of 75054 and 75072 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75054 and 75072. First we will calculate the prime factors of 75054 and 75072.

Prime Factorization of 75054

Prime Factorization of 75072

Now multiplying the highest exponent prime factors to calculate the LCM of 75054 and 75072.

LCM(75054,75072) = 2⁶ × 3¹ × 7¹ × 1787¹ × 17¹ × 23¹
LCM(75054,75072) = 939075648