What is the Least Common Multiple of 804 and 822?

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 804 and 822 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 804 and 822, than apply into the LCM equation.

GCF(804,822) = 6
LCM(804,822) = ( 804 × 822) / 6
LCM(804,822) = 660888 / 6
LCM(804,822) = 110148

Least Common Multiple (LCM) of 804 and 822 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 804 and 822. First we will calculate the prime factors of 804 and 822.

Prime Factorization of 804

Prime Factorization of 822

Now multiplying the highest exponent prime factors to calculate the LCM of 804 and 822.

LCM(804,822) = 2² × 3¹ × 67¹ × 137¹
LCM(804,822) = 110148