What is the Least Common Multiple of 12378 and 12390?

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 12378 and 12390 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12378 and 12390, than apply into the LCM equation.

GCF(12378,12390) = 6
LCM(12378,12390) = ( 12378 × 12390) / 6
LCM(12378,12390) = 153363420 / 6
LCM(12378,12390) = 25560570

Least Common Multiple (LCM) of 12378 and 12390 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12378 and 12390. First we will calculate the prime factors of 12378 and 12390.

Prime Factorization of 12378

Prime Factorization of 12390

Now multiplying the highest exponent prime factors to calculate the LCM of 12378 and 12390.

LCM(12378,12390) = 2¹ × 3¹ × 2063¹ × 5¹ × 7¹ × 59¹
LCM(12378,12390) = 25560570