What is the Least Common Multiple of 15200 and 15214?

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 15200 and 15214 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 15200 and 15214, than apply into the LCM equation.

GCF(15200,15214) = 2
LCM(15200,15214) = ( 15200 × 15214) / 2
LCM(15200,15214) = 231252800 / 2
LCM(15200,15214) = 115626400

Least Common Multiple (LCM) of 15200 and 15214 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 15200 and 15214. First we will calculate the prime factors of 15200 and 15214.

Prime Factorization of 15200

Prime Factorization of 15214

Now multiplying the highest exponent prime factors to calculate the LCM of 15200 and 15214.

LCM(15200,15214) = 2⁵ × 5² × 19¹ × 7607¹
LCM(15200,15214) = 115626400