What is the Least Common Multiple of 71584 and 71600?

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 71584 and 71600 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 71584 and 71600, than apply into the LCM equation.

GCF(71584,71600) = 16
LCM(71584,71600) = ( 71584 × 71600) / 16
LCM(71584,71600) = 5125414400 / 16
LCM(71584,71600) = 320338400

Least Common Multiple (LCM) of 71584 and 71600 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 71584 and 71600. First we will calculate the prime factors of 71584 and 71600.

Prime Factorization of 71584

Prime Factorization of 71600

Now multiplying the highest exponent prime factors to calculate the LCM of 71584 and 71600.

LCM(71584,71600) = 2⁵ × 2237¹ × 5² × 179¹
LCM(71584,71600) = 320338400