What is the Least Common Multiple of 3200 and 3214?

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 3200 and 3214 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3200 and 3214, than apply into the LCM equation.

GCF(3200,3214) = 2
LCM(3200,3214) = ( 3200 × 3214) / 2
LCM(3200,3214) = 10284800 / 2
LCM(3200,3214) = 5142400

Least Common Multiple (LCM) of 3200 and 3214 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3200 and 3214. First we will calculate the prime factors of 3200 and 3214.

Prime Factorization of 3200

Prime Factorization of 3214

Now multiplying the highest exponent prime factors to calculate the LCM of 3200 and 3214.

LCM(3200,3214) = 2⁷ × 5² × 1607¹
LCM(3200,3214) = 5142400