What is the Least Common Multiple of 12300 and 12318?

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 12300 and 12318 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12300 and 12318, than apply into the LCM equation.

GCF(12300,12318) = 6
LCM(12300,12318) = ( 12300 × 12318) / 6
LCM(12300,12318) = 151511400 / 6
LCM(12300,12318) = 25251900

Least Common Multiple (LCM) of 12300 and 12318 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12300 and 12318. First we will calculate the prime factors of 12300 and 12318.

Prime Factorization of 12300

Prime Factorization of 12318

Now multiplying the highest exponent prime factors to calculate the LCM of 12300 and 12318.

LCM(12300,12318) = 2² × 3¹ × 5² × 41¹ × 2053¹
LCM(12300,12318) = 25251900