What is the Least Common Multiple of 6789 and 6804?

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 6789 and 6804 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6789 and 6804, than apply into the LCM equation.

GCF(6789,6804) = 3
LCM(6789,6804) = ( 6789 × 6804) / 3
LCM(6789,6804) = 46192356 / 3
LCM(6789,6804) = 15397452

Least Common Multiple (LCM) of 6789 and 6804 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 6789 and 6804. First we will calculate the prime factors of 6789 and 6804.

Prime Factorization of 6789

Prime Factorization of 6804

Now multiplying the highest exponent prime factors to calculate the LCM of 6789 and 6804.

LCM(6789,6804) = 3⁵ × 31¹ × 73¹ × 2² × 7¹
LCM(6789,6804) = 15397452