What is the Least Common Multiple of 13005 and 13014?

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 13005 and 13014 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13005 and 13014, than apply into the LCM equation.

GCF(13005,13014) = 9
LCM(13005,13014) = ( 13005 × 13014) / 9
LCM(13005,13014) = 169247070 / 9
LCM(13005,13014) = 18805230

Least Common Multiple (LCM) of 13005 and 13014 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13005 and 13014. First we will calculate the prime factors of 13005 and 13014.

Prime Factorization of 13005

Prime Factorization of 13014

Now multiplying the highest exponent prime factors to calculate the LCM of 13005 and 13014.

LCM(13005,13014) = 3³ × 5¹ × 17² × 2¹ × 241¹
LCM(13005,13014) = 18805230