What is the Least Common Multiple of 39584 and 39600?

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 39584 and 39600 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39584 and 39600, than apply into the LCM equation.

GCF(39584,39600) = 16
LCM(39584,39600) = ( 39584 × 39600) / 16
LCM(39584,39600) = 1567526400 / 16
LCM(39584,39600) = 97970400

Least Common Multiple (LCM) of 39584 and 39600 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39584 and 39600. First we will calculate the prime factors of 39584 and 39600.

Prime Factorization of 39584

Prime Factorization of 39600

Now multiplying the highest exponent prime factors to calculate the LCM of 39584 and 39600.

LCM(39584,39600) = 2⁵ × 1237¹ × 3² × 5² × 11¹
LCM(39584,39600) = 97970400