What is the Least Common Multiple of 23400 and 23414?

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 23400 and 23414 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 23400 and 23414, than apply into the LCM equation.

GCF(23400,23414) = 2
LCM(23400,23414) = ( 23400 × 23414) / 2
LCM(23400,23414) = 547887600 / 2
LCM(23400,23414) = 273943800

Least Common Multiple (LCM) of 23400 and 23414 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 23400 and 23414. First we will calculate the prime factors of 23400 and 23414.

Prime Factorization of 23400

Prime Factorization of 23414

Now multiplying the highest exponent prime factors to calculate the LCM of 23400 and 23414.

LCM(23400,23414) = 2³ × 3² × 5² × 13¹ × 23¹ × 509¹
LCM(23400,23414) = 273943800