What is the Least Common Multiple of 8000 and 8004?

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 8000 and 8004 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8000 and 8004, than apply into the LCM equation.

GCF(8000,8004) = 4
LCM(8000,8004) = ( 8000 × 8004) / 4
LCM(8000,8004) = 64032000 / 4
LCM(8000,8004) = 16008000

Least Common Multiple (LCM) of 8000 and 8004 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 8000 and 8004. First we will calculate the prime factors of 8000 and 8004.

Prime Factorization of 8000

Prime Factorization of 8004

Now multiplying the highest exponent prime factors to calculate the LCM of 8000 and 8004.

LCM(8000,8004) = 2⁶ × 5³ × 3¹ × 23¹ × 29¹
LCM(8000,8004) = 16008000