What is the Least Common Multiple of 45084 and 45096?

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 45084 and 45096 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45084 and 45096, than apply into the LCM equation.

GCF(45084,45096) = 12
LCM(45084,45096) = ( 45084 × 45096) / 12
LCM(45084,45096) = 2033108064 / 12
LCM(45084,45096) = 169425672

Least Common Multiple (LCM) of 45084 and 45096 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45084 and 45096. First we will calculate the prime factors of 45084 and 45096.

Prime Factorization of 45084

Prime Factorization of 45096

Now multiplying the highest exponent prime factors to calculate the LCM of 45084 and 45096.

LCM(45084,45096) = 2³ × 3¹ × 13¹ × 17² × 1879¹
LCM(45084,45096) = 169425672