What is the Least Common Multiple of 1996 and 2009?

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 1996 and 2009 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1996 and 2009, than apply into the LCM equation.

GCF(1996,2009) = 1
LCM(1996,2009) = ( 1996 × 2009) / 1
LCM(1996,2009) = 4009964 / 1
LCM(1996,2009) = 4009964

Least Common Multiple (LCM) of 1996 and 2009 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1996 and 2009. First we will calculate the prime factors of 1996 and 2009.

Prime Factorization of 1996

Prime Factorization of 2009

Now multiplying the highest exponent prime factors to calculate the LCM of 1996 and 2009.

LCM(1996,2009) = 2² × 499¹ × 7² × 41¹
LCM(1996,2009) = 4009964