What is the Least Common Multiple of 8200 and 8214?

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 8200 and 8214 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8200 and 8214, than apply into the LCM equation.

GCF(8200,8214) = 2
LCM(8200,8214) = ( 8200 × 8214) / 2
LCM(8200,8214) = 67354800 / 2
LCM(8200,8214) = 33677400

Least Common Multiple (LCM) of 8200 and 8214 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 8200 and 8214. First we will calculate the prime factors of 8200 and 8214.

Prime Factorization of 8200

Prime Factorization of 8214

Now multiplying the highest exponent prime factors to calculate the LCM of 8200 and 8214.

LCM(8200,8214) = 2³ × 5² × 41¹ × 3¹ × 37²
LCM(8200,8214) = 33677400