What is the Least Common Multiple of 12189 and 12200?

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 12189 and 12200 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12189 and 12200, than apply into the LCM equation.

GCF(12189,12200) = 1
LCM(12189,12200) = ( 12189 × 12200) / 1
LCM(12189,12200) = 148705800 / 1
LCM(12189,12200) = 148705800

Least Common Multiple (LCM) of 12189 and 12200 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12189 and 12200. First we will calculate the prime factors of 12189 and 12200.

Prime Factorization of 12189

Prime Factorization of 12200

Now multiplying the highest exponent prime factors to calculate the LCM of 12189 and 12200.

LCM(12189,12200) = 3¹ × 17¹ × 239¹ × 2³ × 5² × 61¹
LCM(12189,12200) = 148705800