What is the Least Common Multiple of 74400 and 74409?

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 74400 and 74409 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 74400 and 74409, than apply into the LCM equation.

GCF(74400,74409) = 3
LCM(74400,74409) = ( 74400 × 74409) / 3
LCM(74400,74409) = 5536029600 / 3
LCM(74400,74409) = 1845343200

Least Common Multiple (LCM) of 74400 and 74409 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 74400 and 74409. First we will calculate the prime factors of 74400 and 74409.

Prime Factorization of 74400

Prime Factorization of 74409

Now multiplying the highest exponent prime factors to calculate the LCM of 74400 and 74409.

LCM(74400,74409) = 2⁵ × 3¹ × 5² × 31¹ × 17¹ × 1459¹
LCM(74400,74409) = 1845343200