What is the Least Common Multiple of 75192 and 75205?

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 75192 and 75205 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75192 and 75205, than apply into the LCM equation.

GCF(75192,75205) = 13
LCM(75192,75205) = ( 75192 × 75205) / 13
LCM(75192,75205) = 5654814360 / 13
LCM(75192,75205) = 434985720

Least Common Multiple (LCM) of 75192 and 75205 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75192 and 75205. First we will calculate the prime factors of 75192 and 75205.

Prime Factorization of 75192

Prime Factorization of 75205

Now multiplying the highest exponent prime factors to calculate the LCM of 75192 and 75205.

LCM(75192,75205) = 2³ × 3¹ × 13² × 241¹ × 5¹ × 89¹
LCM(75192,75205) = 434985720