What is the Least Common Multiple of 82209 and 82221?

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 82221 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 82221, than apply into the LCM equation.

GCF(82209,82221) = 3
LCM(82209,82221) = ( 82209 × 82221) / 3
LCM(82209,82221) = 6759306189 / 3
LCM(82209,82221) = 2253102063

Least Common Multiple (LCM) of 82209 and 82221 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 82209 and 82221. First we will calculate the prime factors of 82209 and 82221.

Prime Factorization of 82209

Prime Factorization of 82221

Now multiplying the highest exponent prime factors to calculate the LCM of 82209 and 82221.

LCM(82209,82221) = 3¹ × 67¹ × 409¹ × 27407¹
LCM(82209,82221) = 2253102063