What is the Least Common Multiple of 82209 and 82224?

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 82209 and 82224 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 82209 and 82224, than apply into the LCM equation.

GCF(82209,82224) = 3
LCM(82209,82224) = ( 82209 × 82224) / 3
LCM(82209,82224) = 6759552816 / 3
LCM(82209,82224) = 2253184272

Least Common Multiple (LCM) of 82209 and 82224 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 82209 and 82224. First we will calculate the prime factors of 82209 and 82224.

Prime Factorization of 82209

Prime Factorization of 82224

Now multiplying the highest exponent prime factors to calculate the LCM of 82209 and 82224.

LCM(82209,82224) = 3² × 67¹ × 409¹ × 2⁴ × 571¹
LCM(82209,82224) = 2253184272