What is the Least Common Multiple of 12096 and 12111?

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 12096 and 12111 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12096 and 12111, than apply into the LCM equation.

GCF(12096,12111) = 3
LCM(12096,12111) = ( 12096 × 12111) / 3
LCM(12096,12111) = 146494656 / 3
LCM(12096,12111) = 48831552

Least Common Multiple (LCM) of 12096 and 12111 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12096 and 12111. First we will calculate the prime factors of 12096 and 12111.

Prime Factorization of 12096

Prime Factorization of 12111

Now multiplying the highest exponent prime factors to calculate the LCM of 12096 and 12111.

LCM(12096,12111) = 2⁶ × 3³ × 7¹ × 11¹ × 367¹
LCM(12096,12111) = 48831552