What is the Least Common Multiple of 2009 and 2028?

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 2009 and 2028 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2009 and 2028, than apply into the LCM equation.

GCF(2009,2028) = 1
LCM(2009,2028) = ( 2009 × 2028) / 1
LCM(2009,2028) = 4074252 / 1
LCM(2009,2028) = 4074252

Least Common Multiple (LCM) of 2009 and 2028 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2009 and 2028. First we will calculate the prime factors of 2009 and 2028.

Prime Factorization of 2009

Prime Factorization of 2028

Now multiplying the highest exponent prime factors to calculate the LCM of 2009 and 2028.

LCM(2009,2028) = 7² × 41¹ × 2² × 3¹ × 13²
LCM(2009,2028) = 4074252