What is the Least Common Multiple of 30304 and 30312?

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 30304 and 30312 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30304 and 30312, than apply into the LCM equation.

GCF(30304,30312) = 8
LCM(30304,30312) = ( 30304 × 30312) / 8
LCM(30304,30312) = 918574848 / 8
LCM(30304,30312) = 114821856

Least Common Multiple (LCM) of 30304 and 30312 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30304 and 30312. First we will calculate the prime factors of 30304 and 30312.

Prime Factorization of 30304

Prime Factorization of 30312

Now multiplying the highest exponent prime factors to calculate the LCM of 30304 and 30312.

LCM(30304,30312) = 2⁵ × 947¹ × 3² × 421¹
LCM(30304,30312) = 114821856