What is the Least Common Multiple of 17856 and 17874?

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 17856 and 17874 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17856 and 17874, than apply into the LCM equation.

GCF(17856,17874) = 18
LCM(17856,17874) = ( 17856 × 17874) / 18
LCM(17856,17874) = 319158144 / 18
LCM(17856,17874) = 17731008

Least Common Multiple (LCM) of 17856 and 17874 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17856 and 17874. First we will calculate the prime factors of 17856 and 17874.

Prime Factorization of 17856

Prime Factorization of 17874

Now multiplying the highest exponent prime factors to calculate the LCM of 17856 and 17874.

LCM(17856,17874) = 2⁶ × 3³ × 31¹ × 331¹
LCM(17856,17874) = 17731008