What is the Least Common Multiple of 19200 and 19214?

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 19214 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 19214, than apply into the LCM equation.

GCF(19200,19214) = 2
LCM(19200,19214) = ( 19200 × 19214) / 2
LCM(19200,19214) = 368908800 / 2
LCM(19200,19214) = 184454400

Least Common Multiple (LCM) of 19200 and 19214 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19200 and 19214. First we will calculate the prime factors of 19200 and 19214.

Prime Factorization of 19200

Prime Factorization of 19214

Now multiplying the highest exponent prime factors to calculate the LCM of 19200 and 19214.

LCM(19200,19214) = 2⁸ × 3¹ × 5² × 13¹ × 739¹
LCM(19200,19214) = 184454400