What is the Least Common Multiple of 30288 and 30304?

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 30288 and 30304 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30288 and 30304, than apply into the LCM equation.

GCF(30288,30304) = 16
LCM(30288,30304) = ( 30288 × 30304) / 16
LCM(30288,30304) = 917847552 / 16
LCM(30288,30304) = 57365472

Least Common Multiple (LCM) of 30288 and 30304 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30288 and 30304. First we will calculate the prime factors of 30288 and 30304.

Prime Factorization of 30288

Prime Factorization of 30304

Now multiplying the highest exponent prime factors to calculate the LCM of 30288 and 30304.

LCM(30288,30304) = 2⁵ × 3¹ × 631¹ × 947¹
LCM(30288,30304) = 57365472