What is the Least Common Multiple of 87584 and 87600?

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 87584 and 87600 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 87584 and 87600, than apply into the LCM equation.

GCF(87584,87600) = 16
LCM(87584,87600) = ( 87584 × 87600) / 16
LCM(87584,87600) = 7672358400 / 16
LCM(87584,87600) = 479522400

Least Common Multiple (LCM) of 87584 and 87600 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 87584 and 87600. First we will calculate the prime factors of 87584 and 87600.

Prime Factorization of 87584

Prime Factorization of 87600

Now multiplying the highest exponent prime factors to calculate the LCM of 87584 and 87600.

LCM(87584,87600) = 2⁵ × 7¹ × 17¹ × 23¹ × 3¹ × 5² × 73¹
LCM(87584,87600) = 479522400