What is the Least Common Multiple of 6804 and 6822?

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 6804 and 6822 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6804 and 6822, than apply into the LCM equation.

GCF(6804,6822) = 18
LCM(6804,6822) = ( 6804 × 6822) / 18
LCM(6804,6822) = 46416888 / 18
LCM(6804,6822) = 2578716

Least Common Multiple (LCM) of 6804 and 6822 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 6804 and 6822. First we will calculate the prime factors of 6804 and 6822.

Prime Factorization of 6804

Prime Factorization of 6822

Now multiplying the highest exponent prime factors to calculate the LCM of 6804 and 6822.

LCM(6804,6822) = 2² × 3⁵ × 7¹ × 379¹
LCM(6804,6822) = 2578716