What is the Least Common Multiple of 1872 and 1889?

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 1872 and 1889 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1872 and 1889, than apply into the LCM equation.

GCF(1872,1889) = 1
LCM(1872,1889) = ( 1872 × 1889) / 1
LCM(1872,1889) = 3536208 / 1
LCM(1872,1889) = 3536208

Least Common Multiple (LCM) of 1872 and 1889 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1872 and 1889. First we will calculate the prime factors of 1872 and 1889.

Prime Factorization of 1872

Prime Factorization of 1889

Now multiplying the highest exponent prime factors to calculate the LCM of 1872 and 1889.

LCM(1872,1889) = 2⁴ × 3² × 13¹ × 1889¹
LCM(1872,1889) = 3536208