What is the Least Common Multiple of 28400 and 28414?

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 28400 and 28414 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 28400 and 28414, than apply into the LCM equation.

GCF(28400,28414) = 2
LCM(28400,28414) = ( 28400 × 28414) / 2
LCM(28400,28414) = 806957600 / 2
LCM(28400,28414) = 403478800

Least Common Multiple (LCM) of 28400 and 28414 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 28400 and 28414. First we will calculate the prime factors of 28400 and 28414.

Prime Factorization of 28400

Prime Factorization of 28414

Now multiplying the highest exponent prime factors to calculate the LCM of 28400 and 28414.

LCM(28400,28414) = 2⁴ × 5² × 71¹ × 14207¹
LCM(28400,28414) = 403478800