What is the Least Common Multiple of 3075 and 3084?

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 3075 and 3084 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3075 and 3084, than apply into the LCM equation.

GCF(3075,3084) = 3
LCM(3075,3084) = ( 3075 × 3084) / 3
LCM(3075,3084) = 9483300 / 3
LCM(3075,3084) = 3161100

Least Common Multiple (LCM) of 3075 and 3084 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3075 and 3084. First we will calculate the prime factors of 3075 and 3084.

Prime Factorization of 3075

Prime Factorization of 3084

Now multiplying the highest exponent prime factors to calculate the LCM of 3075 and 3084.

LCM(3075,3084) = 3¹ × 5² × 41¹ × 2² × 257¹
LCM(3075,3084) = 3161100