What is the Least Common Multiple of 12069 and 12075?

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 12069 and 12075 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12069 and 12075, than apply into the LCM equation.

GCF(12069,12075) = 3
LCM(12069,12075) = ( 12069 × 12075) / 3
LCM(12069,12075) = 145733175 / 3
LCM(12069,12075) = 48577725

Least Common Multiple (LCM) of 12069 and 12075 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12069 and 12075. First we will calculate the prime factors of 12069 and 12075.

Prime Factorization of 12069

Prime Factorization of 12075

Now multiplying the highest exponent prime factors to calculate the LCM of 12069 and 12075.

LCM(12069,12075) = 3⁴ × 149¹ × 5² × 7¹ × 23¹
LCM(12069,12075) = 48577725