What is the Least Common Multiple of 19200 and 19215?

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 19200 and 19215 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19200 and 19215, than apply into the LCM equation.

GCF(19200,19215) = 15
LCM(19200,19215) = ( 19200 × 19215) / 15
LCM(19200,19215) = 368928000 / 15
LCM(19200,19215) = 24595200

Least Common Multiple (LCM) of 19200 and 19215 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19200 and 19215. First we will calculate the prime factors of 19200 and 19215.

Prime Factorization of 19200

Prime Factorization of 19215

Now multiplying the highest exponent prime factors to calculate the LCM of 19200 and 19215.

LCM(19200,19215) = 2⁸ × 3² × 5² × 7¹ × 61¹
LCM(19200,19215) = 24595200