What is the Least Common Multiple of 83200 and 83214?

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 83200 and 83214 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 83200 and 83214, than apply into the LCM equation.

GCF(83200,83214) = 2
LCM(83200,83214) = ( 83200 × 83214) / 2
LCM(83200,83214) = 6923404800 / 2
LCM(83200,83214) = 3461702400

Least Common Multiple (LCM) of 83200 and 83214 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 83200 and 83214. First we will calculate the prime factors of 83200 and 83214.

Prime Factorization of 83200

Prime Factorization of 83214

Now multiplying the highest exponent prime factors to calculate the LCM of 83200 and 83214.

LCM(83200,83214) = 2⁸ × 5² × 13¹ × 3³ × 23¹ × 67¹
LCM(83200,83214) = 3461702400