What is the Least Common Multiple of 85800 and 85814?

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 85800 and 85814 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 85800 and 85814, than apply into the LCM equation.

GCF(85800,85814) = 2
LCM(85800,85814) = ( 85800 × 85814) / 2
LCM(85800,85814) = 7362841200 / 2
LCM(85800,85814) = 3681420600

Least Common Multiple (LCM) of 85800 and 85814 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 85800 and 85814. First we will calculate the prime factors of 85800 and 85814.

Prime Factorization of 85800

Prime Factorization of 85814

Now multiplying the highest exponent prime factors to calculate the LCM of 85800 and 85814.

LCM(85800,85814) = 2³ × 3¹ × 5² × 11¹ × 13¹ × 107¹ × 401¹
LCM(85800,85814) = 3681420600