What is the Least Common Multiple of 19188 and 19200?

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 19188 and 19200 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19188 and 19200, than apply into the LCM equation.

GCF(19188,19200) = 12
LCM(19188,19200) = ( 19188 × 19200) / 12
LCM(19188,19200) = 368409600 / 12
LCM(19188,19200) = 30700800

Least Common Multiple (LCM) of 19188 and 19200 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19188 and 19200. First we will calculate the prime factors of 19188 and 19200.

Prime Factorization of 19188

Prime Factorization of 19200

Now multiplying the highest exponent prime factors to calculate the LCM of 19188 and 19200.

LCM(19188,19200) = 2⁸ × 3² × 13¹ × 41¹ × 5²
LCM(19188,19200) = 30700800