What is the Least Common Multiple of 1899 and 1908?

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 1899 and 1908 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1899 and 1908, than apply into the LCM equation.

GCF(1899,1908) = 9
LCM(1899,1908) = ( 1899 × 1908) / 9
LCM(1899,1908) = 3623292 / 9
LCM(1899,1908) = 402588

Least Common Multiple (LCM) of 1899 and 1908 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1899 and 1908. First we will calculate the prime factors of 1899 and 1908.

Prime Factorization of 1899

Prime Factorization of 1908

Now multiplying the highest exponent prime factors to calculate the LCM of 1899 and 1908.

LCM(1899,1908) = 3² × 211¹ × 2² × 53¹
LCM(1899,1908) = 402588