What is the Least Common Multiple of 54400 and 54414?

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 54400 and 54414 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54400 and 54414, than apply into the LCM equation.

GCF(54400,54414) = 2
LCM(54400,54414) = ( 54400 × 54414) / 2
LCM(54400,54414) = 2960121600 / 2
LCM(54400,54414) = 1480060800

Least Common Multiple (LCM) of 54400 and 54414 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54400 and 54414. First we will calculate the prime factors of 54400 and 54414.

Prime Factorization of 54400

Prime Factorization of 54414

Now multiplying the highest exponent prime factors to calculate the LCM of 54400 and 54414.

LCM(54400,54414) = 2⁷ × 5² × 17¹ × 3² × 3023¹
LCM(54400,54414) = 1480060800