What is the Least Common Multiple of 12075 and 12084?

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 12075 and 12084 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12075 and 12084, than apply into the LCM equation.

GCF(12075,12084) = 3
LCM(12075,12084) = ( 12075 × 12084) / 3
LCM(12075,12084) = 145914300 / 3
LCM(12075,12084) = 48638100

Least Common Multiple (LCM) of 12075 and 12084 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12075 and 12084. First we will calculate the prime factors of 12075 and 12084.

Prime Factorization of 12075

Prime Factorization of 12084

Now multiplying the highest exponent prime factors to calculate the LCM of 12075 and 12084.

LCM(12075,12084) = 3¹ × 5² × 7¹ × 23¹ × 2² × 19¹ × 53¹
LCM(12075,12084) = 48638100