What is the Least Common Multiple of 12210 and 12214?

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 12210 and 12214 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12210 and 12214, than apply into the LCM equation.

GCF(12210,12214) = 2
LCM(12210,12214) = ( 12210 × 12214) / 2
LCM(12210,12214) = 149132940 / 2
LCM(12210,12214) = 74566470

Least Common Multiple (LCM) of 12210 and 12214 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12210 and 12214. First we will calculate the prime factors of 12210 and 12214.

Prime Factorization of 12210

Prime Factorization of 12214

Now multiplying the highest exponent prime factors to calculate the LCM of 12210 and 12214.

LCM(12210,12214) = 2¹ × 3¹ × 5¹ × 11¹ × 37¹ × 31¹ × 197¹
LCM(12210,12214) = 74566470