What is the Least Common Multiple of 76800 and 76814?

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 76800 and 76814 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 76800 and 76814, than apply into the LCM equation.

GCF(76800,76814) = 2
LCM(76800,76814) = ( 76800 × 76814) / 2
LCM(76800,76814) = 5899315200 / 2
LCM(76800,76814) = 2949657600

Least Common Multiple (LCM) of 76800 and 76814 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 76800 and 76814. First we will calculate the prime factors of 76800 and 76814.

Prime Factorization of 76800

Prime Factorization of 76814

Now multiplying the highest exponent prime factors to calculate the LCM of 76800 and 76814.

LCM(76800,76814) = 2¹⁰ × 3¹ × 5² × 193¹ × 199¹
LCM(76800,76814) = 2949657600