What is the Least Common Multiple of 13200 and 13214?

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 13200 and 13214 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13200 and 13214, than apply into the LCM equation.

GCF(13200,13214) = 2
LCM(13200,13214) = ( 13200 × 13214) / 2
LCM(13200,13214) = 174424800 / 2
LCM(13200,13214) = 87212400

Least Common Multiple (LCM) of 13200 and 13214 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13200 and 13214. First we will calculate the prime factors of 13200 and 13214.

Prime Factorization of 13200

Prime Factorization of 13214

Now multiplying the highest exponent prime factors to calculate the LCM of 13200 and 13214.

LCM(13200,13214) = 2⁴ × 3¹ × 5² × 11¹ × 6607¹
LCM(13200,13214) = 87212400