What is the Least Common Multiple of 8004 and 8008?

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 8008 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 8008, than apply into the LCM equation.

GCF(8004,8008) = 4
LCM(8004,8008) = ( 8004 × 8008) / 4
LCM(8004,8008) = 64096032 / 4
LCM(8004,8008) = 16024008

Least Common Multiple (LCM) of 8004 and 8008 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 8004 and 8008. First we will calculate the prime factors of 8004 and 8008.

Prime Factorization of 8004

Prime Factorization of 8008

Now multiplying the highest exponent prime factors to calculate the LCM of 8004 and 8008.

LCM(8004,8008) = 2³ × 3¹ × 23¹ × 29¹ × 7¹ × 11¹ × 13¹
LCM(8004,8008) = 16024008