What is the Least Common Multiple of 1900 and 1909?

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 1900 and 1909 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1900 and 1909, than apply into the LCM equation.

GCF(1900,1909) = 1
LCM(1900,1909) = ( 1900 × 1909) / 1
LCM(1900,1909) = 3627100 / 1
LCM(1900,1909) = 3627100

Least Common Multiple (LCM) of 1900 and 1909 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1900 and 1909. First we will calculate the prime factors of 1900 and 1909.

Prime Factorization of 1900

Prime Factorization of 1909

Now multiplying the highest exponent prime factors to calculate the LCM of 1900 and 1909.

LCM(1900,1909) = 2² × 5² × 19¹ × 23¹ × 83¹
LCM(1900,1909) = 3627100