What is the Least Common Multiple of 12075 and 12090?

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 12090 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 12090, than apply into the LCM equation.

GCF(12075,12090) = 15
LCM(12075,12090) = ( 12075 × 12090) / 15
LCM(12075,12090) = 145986750 / 15
LCM(12075,12090) = 9732450

Least Common Multiple (LCM) of 12075 and 12090 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12075 and 12090. First we will calculate the prime factors of 12075 and 12090.

Prime Factorization of 12075

Prime Factorization of 12090

Now multiplying the highest exponent prime factors to calculate the LCM of 12075 and 12090.

LCM(12075,12090) = 3¹ × 5² × 7¹ × 23¹ × 2¹ × 13¹ × 31¹
LCM(12075,12090) = 9732450