What is the Least Common Multiple of 16800 and 16814?

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 16800 and 16814 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 16800 and 16814, than apply into the LCM equation.

GCF(16800,16814) = 14
LCM(16800,16814) = ( 16800 × 16814) / 14
LCM(16800,16814) = 282475200 / 14
LCM(16800,16814) = 20176800

Least Common Multiple (LCM) of 16800 and 16814 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 16800 and 16814. First we will calculate the prime factors of 16800 and 16814.

Prime Factorization of 16800

Prime Factorization of 16814

Now multiplying the highest exponent prime factors to calculate the LCM of 16800 and 16814.

LCM(16800,16814) = 2⁵ × 3¹ × 5² × 7¹ × 1201¹
LCM(16800,16814) = 20176800