What is the Least Common Multiple of 8204 and 8224?

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 8204 and 8224 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8204 and 8224, than apply into the LCM equation.

GCF(8204,8224) = 4
LCM(8204,8224) = ( 8204 × 8224) / 4
LCM(8204,8224) = 67469696 / 4
LCM(8204,8224) = 16867424

Least Common Multiple (LCM) of 8204 and 8224 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 8204 and 8224. First we will calculate the prime factors of 8204 and 8224.

Prime Factorization of 8204

Prime Factorization of 8224

Now multiplying the highest exponent prime factors to calculate the LCM of 8204 and 8224.

LCM(8204,8224) = 2⁵ × 7¹ × 293¹ × 257¹
LCM(8204,8224) = 16867424