What is the Least Common Multiple of 34200 and 34214?

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 34200 and 34214 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 34200 and 34214, than apply into the LCM equation.

GCF(34200,34214) = 2
LCM(34200,34214) = ( 34200 × 34214) / 2
LCM(34200,34214) = 1170118800 / 2
LCM(34200,34214) = 585059400

Least Common Multiple (LCM) of 34200 and 34214 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 34200 and 34214. First we will calculate the prime factors of 34200 and 34214.

Prime Factorization of 34200

Prime Factorization of 34214

Now multiplying the highest exponent prime factors to calculate the LCM of 34200 and 34214.

LCM(34200,34214) = 2³ × 3² × 5² × 19¹ × 17107¹
LCM(34200,34214) = 585059400