What is the Least Common Multiple of 14400 and 14414?

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 14400 and 14414 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 14400 and 14414, than apply into the LCM equation.

GCF(14400,14414) = 2
LCM(14400,14414) = ( 14400 × 14414) / 2
LCM(14400,14414) = 207561600 / 2
LCM(14400,14414) = 103780800

Least Common Multiple (LCM) of 14400 and 14414 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 14400 and 14414. First we will calculate the prime factors of 14400 and 14414.

Prime Factorization of 14400

Prime Factorization of 14414

Now multiplying the highest exponent prime factors to calculate the LCM of 14400 and 14414.

LCM(14400,14414) = 2⁶ × 3² × 5² × 7207¹
LCM(14400,14414) = 103780800