What is the Least Common Multiple of 57200 and 57214?

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 57200 and 57214 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 57200 and 57214, than apply into the LCM equation.

GCF(57200,57214) = 2
LCM(57200,57214) = ( 57200 × 57214) / 2
LCM(57200,57214) = 3272640800 / 2
LCM(57200,57214) = 1636320400

Least Common Multiple (LCM) of 57200 and 57214 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 57200 and 57214. First we will calculate the prime factors of 57200 and 57214.

Prime Factorization of 57200

Prime Factorization of 57214

Now multiplying the highest exponent prime factors to calculate the LCM of 57200 and 57214.

LCM(57200,57214) = 2⁴ × 5² × 11¹ × 13¹ × 28607¹
LCM(57200,57214) = 1636320400