What is the Least Common Multiple of 12189 and 12208?

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 12208 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 12208, than apply into the LCM equation.

GCF(12189,12208) = 1
LCM(12189,12208) = ( 12189 × 12208) / 1
LCM(12189,12208) = 148803312 / 1
LCM(12189,12208) = 148803312

Least Common Multiple (LCM) of 12189 and 12208 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12189 and 12208. First we will calculate the prime factors of 12189 and 12208.

Prime Factorization of 12189

Prime Factorization of 12208

Now multiplying the highest exponent prime factors to calculate the LCM of 12189 and 12208.

LCM(12189,12208) = 3¹ × 17¹ × 239¹ × 2⁴ × 7¹ × 109¹
LCM(12189,12208) = 148803312