What is the Least Common Multiple of 45594 and 45600?

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 45594 and 45600 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45594 and 45600, than apply into the LCM equation.

GCF(45594,45600) = 6
LCM(45594,45600) = ( 45594 × 45600) / 6
LCM(45594,45600) = 2079086400 / 6
LCM(45594,45600) = 346514400

Least Common Multiple (LCM) of 45594 and 45600 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45594 and 45600. First we will calculate the prime factors of 45594 and 45600.

Prime Factorization of 45594

Prime Factorization of 45600

Now multiplying the highest exponent prime factors to calculate the LCM of 45594 and 45600.

LCM(45594,45600) = 2⁵ × 3² × 17¹ × 149¹ × 5² × 19¹
LCM(45594,45600) = 346514400