What is the Least Common Multiple of 18900 and 18912?

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 18900 and 18912 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 18900 and 18912, than apply into the LCM equation.

GCF(18900,18912) = 12
LCM(18900,18912) = ( 18900 × 18912) / 12
LCM(18900,18912) = 357436800 / 12
LCM(18900,18912) = 29786400

Least Common Multiple (LCM) of 18900 and 18912 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 18900 and 18912. First we will calculate the prime factors of 18900 and 18912.

Prime Factorization of 18900

Prime Factorization of 18912

Now multiplying the highest exponent prime factors to calculate the LCM of 18900 and 18912.

LCM(18900,18912) = 2⁵ × 3³ × 5² × 7¹ × 197¹
LCM(18900,18912) = 29786400