What is the Least Common Multiple of 85854 and 85872?

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 85854 and 85872 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 85854 and 85872, than apply into the LCM equation.

GCF(85854,85872) = 6
LCM(85854,85872) = ( 85854 × 85872) / 6
LCM(85854,85872) = 7372454688 / 6
LCM(85854,85872) = 1228742448

Least Common Multiple (LCM) of 85854 and 85872 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 85854 and 85872. First we will calculate the prime factors of 85854 and 85872.

Prime Factorization of 85854

Prime Factorization of 85872

Now multiplying the highest exponent prime factors to calculate the LCM of 85854 and 85872.

LCM(85854,85872) = 2⁴ × 3¹ × 41¹ × 349¹ × 1789¹
LCM(85854,85872) = 1228742448