What is the Least Common Multiple of 12345 and 12360?

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 12345 and 12360 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12345 and 12360, than apply into the LCM equation.

GCF(12345,12360) = 15
LCM(12345,12360) = ( 12345 × 12360) / 15
LCM(12345,12360) = 152584200 / 15
LCM(12345,12360) = 10172280

Least Common Multiple (LCM) of 12345 and 12360 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12345 and 12360. First we will calculate the prime factors of 12345 and 12360.

Prime Factorization of 12345

Prime Factorization of 12360

Now multiplying the highest exponent prime factors to calculate the LCM of 12345 and 12360.

LCM(12345,12360) = 3¹ × 5¹ × 823¹ × 2³ × 103¹
LCM(12345,12360) = 10172280