What is the Least Common Multiple of 76800 and 76804?

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 76804 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 76804, than apply into the LCM equation.

GCF(76800,76804) = 4
LCM(76800,76804) = ( 76800 × 76804) / 4
LCM(76800,76804) = 5898547200 / 4
LCM(76800,76804) = 1474636800

Least Common Multiple (LCM) of 76800 and 76804 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 76800 and 76804. First we will calculate the prime factors of 76800 and 76804.

Prime Factorization of 76800

Prime Factorization of 76804

Now multiplying the highest exponent prime factors to calculate the LCM of 76800 and 76804.

LCM(76800,76804) = 2¹⁰ × 3¹ × 5² × 7¹ × 13¹ × 211¹
LCM(76800,76804) = 1474636800