What is the Least Common Multiple of 45084 and 45102?

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 45102 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 45102, than apply into the LCM equation.

GCF(45084,45102) = 6
LCM(45084,45102) = ( 45084 × 45102) / 6
LCM(45084,45102) = 2033378568 / 6
LCM(45084,45102) = 338896428

Least Common Multiple (LCM) of 45084 and 45102 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45084 and 45102. First we will calculate the prime factors of 45084 and 45102.

Prime Factorization of 45084

Prime Factorization of 45102

Now multiplying the highest exponent prime factors to calculate the LCM of 45084 and 45102.

LCM(45084,45102) = 2² × 3¹ × 13¹ × 17² × 7517¹
LCM(45084,45102) = 338896428