What is the Least Common Multiple of 90288 and 90304?

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 90288 and 90304 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 90288 and 90304, than apply into the LCM equation.

GCF(90288,90304) = 16
LCM(90288,90304) = ( 90288 × 90304) / 16
LCM(90288,90304) = 8153367552 / 16
LCM(90288,90304) = 509585472

Least Common Multiple (LCM) of 90288 and 90304 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 90288 and 90304. First we will calculate the prime factors of 90288 and 90304.

Prime Factorization of 90288

Prime Factorization of 90304

Now multiplying the highest exponent prime factors to calculate the LCM of 90288 and 90304.

LCM(90288,90304) = 2⁶ × 3³ × 11¹ × 19¹ × 17¹ × 83¹
LCM(90288,90304) = 509585472