What is the Least Common Multiple of 12096 and 12105?

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 12105 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 12105, than apply into the LCM equation.

GCF(12096,12105) = 9
LCM(12096,12105) = ( 12096 × 12105) / 9
LCM(12096,12105) = 146422080 / 9
LCM(12096,12105) = 16269120

Least Common Multiple (LCM) of 12096 and 12105 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12096 and 12105. First we will calculate the prime factors of 12096 and 12105.

Prime Factorization of 12096

Prime Factorization of 12105

Now multiplying the highest exponent prime factors to calculate the LCM of 12096 and 12105.

LCM(12096,12105) = 2⁶ × 3³ × 7¹ × 5¹ × 269¹
LCM(12096,12105) = 16269120