What is the Least Common Multiple of 31209 and 31214?

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 31209 and 31214 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31209 and 31214, than apply into the LCM equation.

GCF(31209,31214) = 1
LCM(31209,31214) = ( 31209 × 31214) / 1
LCM(31209,31214) = 974157726 / 1
LCM(31209,31214) = 974157726

Least Common Multiple (LCM) of 31209 and 31214 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31209 and 31214. First we will calculate the prime factors of 31209 and 31214.

Prime Factorization of 31209

Prime Factorization of 31214

Now multiplying the highest exponent prime factors to calculate the LCM of 31209 and 31214.

LCM(31209,31214) = 3¹ × 101¹ × 103¹ × 2¹ × 15607¹
LCM(31209,31214) = 974157726