What is the Least Common Multiple of 800 and 814?

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 800 and 814 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 800 and 814, than apply into the LCM equation.

GCF(800,814) = 2
LCM(800,814) = ( 800 × 814) / 2
LCM(800,814) = 651200 / 2
LCM(800,814) = 325600

Least Common Multiple (LCM) of 800 and 814 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 800 and 814. First we will calculate the prime factors of 800 and 814.

Prime Factorization of 800

Prime Factorization of 814

Now multiplying the highest exponent prime factors to calculate the LCM of 800 and 814.

LCM(800,814) = 2⁵ × 5² × 11¹ × 37¹
LCM(800,814) = 325600