What is the Least Common Multiple of 6400 and 6414?

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 6400 and 6414 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6400 and 6414, than apply into the LCM equation.

GCF(6400,6414) = 2
LCM(6400,6414) = ( 6400 × 6414) / 2
LCM(6400,6414) = 41049600 / 2
LCM(6400,6414) = 20524800

Least Common Multiple (LCM) of 6400 and 6414 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 6400 and 6414. First we will calculate the prime factors of 6400 and 6414.

Prime Factorization of 6400

Prime Factorization of 6414

Now multiplying the highest exponent prime factors to calculate the LCM of 6400 and 6414.

LCM(6400,6414) = 2⁸ × 5² × 3¹ × 1069¹
LCM(6400,6414) = 20524800