What is the Least Common Multiple of 13000 and 13005?

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 13000 and 13005 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13000 and 13005, than apply into the LCM equation.

GCF(13000,13005) = 5
LCM(13000,13005) = ( 13000 × 13005) / 5
LCM(13000,13005) = 169065000 / 5
LCM(13000,13005) = 33813000

Least Common Multiple (LCM) of 13000 and 13005 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13000 and 13005. First we will calculate the prime factors of 13000 and 13005.

Prime Factorization of 13000

Prime Factorization of 13005

Now multiplying the highest exponent prime factors to calculate the LCM of 13000 and 13005.

LCM(13000,13005) = 2³ × 5³ × 13¹ × 3² × 17²
LCM(13000,13005) = 33813000