What is the Least Common Multiple of 2109 and 2123?

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 2109 and 2123 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2109 and 2123, than apply into the LCM equation.

GCF(2109,2123) = 1
LCM(2109,2123) = ( 2109 × 2123) / 1
LCM(2109,2123) = 4477407 / 1
LCM(2109,2123) = 4477407

Least Common Multiple (LCM) of 2109 and 2123 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2109 and 2123. First we will calculate the prime factors of 2109 and 2123.

Prime Factorization of 2109

Prime Factorization of 2123

Now multiplying the highest exponent prime factors to calculate the LCM of 2109 and 2123.

LCM(2109,2123) = 3¹ × 19¹ × 37¹ × 11¹ × 193¹
LCM(2109,2123) = 4477407