What is the Least Common Multiple of 189 and 209?

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 189 and 209 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 189 and 209, than apply into the LCM equation.

GCF(189,209) = 1
LCM(189,209) = ( 189 × 209) / 1
LCM(189,209) = 39501 / 1
LCM(189,209) = 39501

Least Common Multiple (LCM) of 189 and 209 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 189 and 209. First we will calculate the prime factors of 189 and 209.

Prime Factorization of 189

Prime Factorization of 209

Now multiplying the highest exponent prime factors to calculate the LCM of 189 and 209.

LCM(189,209) = 3³ × 7¹ × 11¹ × 19¹
LCM(189,209) = 39501