What is the Least Common Multiple of 34194 and 34200?

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 34194 and 34200 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 34194 and 34200, than apply into the LCM equation.

GCF(34194,34200) = 6
LCM(34194,34200) = ( 34194 × 34200) / 6
LCM(34194,34200) = 1169434800 / 6
LCM(34194,34200) = 194905800

Least Common Multiple (LCM) of 34194 and 34200 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 34194 and 34200. First we will calculate the prime factors of 34194 and 34200.

Prime Factorization of 34194

Prime Factorization of 34200

Now multiplying the highest exponent prime factors to calculate the LCM of 34194 and 34200.

LCM(34194,34200) = 2³ × 3² × 41¹ × 139¹ × 5² × 19¹
LCM(34194,34200) = 194905800