What is the Least Common Multiple of 43200 and 43214?

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 43200 and 43214 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 43200 and 43214, than apply into the LCM equation.

GCF(43200,43214) = 2
LCM(43200,43214) = ( 43200 × 43214) / 2
LCM(43200,43214) = 1866844800 / 2
LCM(43200,43214) = 933422400

Least Common Multiple (LCM) of 43200 and 43214 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 43200 and 43214. First we will calculate the prime factors of 43200 and 43214.

Prime Factorization of 43200

Prime Factorization of 43214

Now multiplying the highest exponent prime factors to calculate the LCM of 43200 and 43214.

LCM(43200,43214) = 2⁶ × 3³ × 5² × 17¹ × 31¹ × 41¹
LCM(43200,43214) = 933422400