What is the Least Common Multiple of 75264 and 75269?

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 75269 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 75269, than apply into the LCM equation.

GCF(75264,75269) = 1
LCM(75264,75269) = ( 75264 × 75269) / 1
LCM(75264,75269) = 5665046016 / 1
LCM(75264,75269) = 5665046016

Least Common Multiple (LCM) of 75264 and 75269 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75264 and 75269. First we will calculate the prime factors of 75264 and 75269.

Prime Factorization of 75264

Prime Factorization of 75269

Now multiplying the highest exponent prime factors to calculate the LCM of 75264 and 75269.

LCM(75264,75269) = 2⁹ × 3¹ × 7² × 75269¹
LCM(75264,75269) = 5665046016