What is the Least Common Multiple of 4000 and 4008?

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 4000 and 4008 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 4000 and 4008, than apply into the LCM equation.

GCF(4000,4008) = 8
LCM(4000,4008) = ( 4000 × 4008) / 8
LCM(4000,4008) = 16032000 / 8
LCM(4000,4008) = 2004000

Least Common Multiple (LCM) of 4000 and 4008 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 4000 and 4008. First we will calculate the prime factors of 4000 and 4008.

Prime Factorization of 4000

Prime Factorization of 4008

Now multiplying the highest exponent prime factors to calculate the LCM of 4000 and 4008.

LCM(4000,4008) = 2⁵ × 5³ × 3¹ × 167¹
LCM(4000,4008) = 2004000