What is the Least Common Multiple of 2005 and 2013?

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 2005 and 2013 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2005 and 2013, than apply into the LCM equation.

GCF(2005,2013) = 1
LCM(2005,2013) = ( 2005 × 2013) / 1
LCM(2005,2013) = 4036065 / 1
LCM(2005,2013) = 4036065

Least Common Multiple (LCM) of 2005 and 2013 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2005 and 2013. First we will calculate the prime factors of 2005 and 2013.

Prime Factorization of 2005

Prime Factorization of 2013

Now multiplying the highest exponent prime factors to calculate the LCM of 2005 and 2013.

LCM(2005,2013) = 5¹ × 401¹ × 3¹ × 11¹ × 61¹
LCM(2005,2013) = 4036065