What is the Least Common Multiple of 12209 and 12213?

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 12209 and 12213 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12209 and 12213, than apply into the LCM equation.

GCF(12209,12213) = 1
LCM(12209,12213) = ( 12209 × 12213) / 1
LCM(12209,12213) = 149108517 / 1
LCM(12209,12213) = 149108517

Least Common Multiple (LCM) of 12209 and 12213 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12209 and 12213. First we will calculate the prime factors of 12209 and 12213.

Prime Factorization of 12209

Prime Factorization of 12213

Now multiplying the highest exponent prime factors to calculate the LCM of 12209 and 12213.

LCM(12209,12213) = 29¹ × 421¹ × 3² × 23¹ × 59¹
LCM(12209,12213) = 149108517