What is the Least Common Multiple of 18400 and 18414?

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 18400 and 18414 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 18400 and 18414, than apply into the LCM equation.

GCF(18400,18414) = 2
LCM(18400,18414) = ( 18400 × 18414) / 2
LCM(18400,18414) = 338817600 / 2
LCM(18400,18414) = 169408800

Least Common Multiple (LCM) of 18400 and 18414 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 18400 and 18414. First we will calculate the prime factors of 18400 and 18414.

Prime Factorization of 18400

Prime Factorization of 18414

Now multiplying the highest exponent prime factors to calculate the LCM of 18400 and 18414.

LCM(18400,18414) = 2⁵ × 5² × 23¹ × 3³ × 11¹ × 31¹
LCM(18400,18414) = 169408800