What is the Least Common Multiple of 45096 and 45114?

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 45096 and 45114 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45096 and 45114, than apply into the LCM equation.

GCF(45096,45114) = 6
LCM(45096,45114) = ( 45096 × 45114) / 6
LCM(45096,45114) = 2034460944 / 6
LCM(45096,45114) = 339076824

Least Common Multiple (LCM) of 45096 and 45114 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45096 and 45114. First we will calculate the prime factors of 45096 and 45114.

Prime Factorization of 45096

Prime Factorization of 45114

Now multiplying the highest exponent prime factors to calculate the LCM of 45096 and 45114.

LCM(45096,45114) = 2³ × 3¹ × 1879¹ × 73¹ × 103¹
LCM(45096,45114) = 339076824