What is the Least Common Multiple of 75264 and 75270?

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 75264 and 75270 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75264 and 75270, than apply into the LCM equation.

GCF(75264,75270) = 6
LCM(75264,75270) = ( 75264 × 75270) / 6
LCM(75264,75270) = 5665121280 / 6
LCM(75264,75270) = 944186880

Least Common Multiple (LCM) of 75264 and 75270 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75264 and 75270. First we will calculate the prime factors of 75264 and 75270.

Prime Factorization of 75264

Prime Factorization of 75270

Now multiplying the highest exponent prime factors to calculate the LCM of 75264 and 75270.

LCM(75264,75270) = 2⁹ × 3¹ × 7² × 5¹ × 13¹ × 193¹
LCM(75264,75270) = 944186880