What is the Least Common Multiple of 8004 and 8012?

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 8004 and 8012 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8004 and 8012, than apply into the LCM equation.

GCF(8004,8012) = 4
LCM(8004,8012) = ( 8004 × 8012) / 4
LCM(8004,8012) = 64128048 / 4
LCM(8004,8012) = 16032012

Least Common Multiple (LCM) of 8004 and 8012 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 8004 and 8012. First we will calculate the prime factors of 8004 and 8012.

Prime Factorization of 8004

Prime Factorization of 8012

Now multiplying the highest exponent prime factors to calculate the LCM of 8004 and 8012.

LCM(8004,8012) = 2² × 3¹ × 23¹ × 29¹ × 2003¹
LCM(8004,8012) = 16032012