What is the Least Common Multiple of 82112 and 82116?

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 82112 and 82116 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 82112 and 82116, than apply into the LCM equation.

GCF(82112,82116) = 4
LCM(82112,82116) = ( 82112 × 82116) / 4
LCM(82112,82116) = 6742708992 / 4
LCM(82112,82116) = 1685677248

Least Common Multiple (LCM) of 82112 and 82116 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 82112 and 82116. First we will calculate the prime factors of 82112 and 82116.

Prime Factorization of 82112

Prime Factorization of 82116

Now multiplying the highest exponent prime factors to calculate the LCM of 82112 and 82116.

LCM(82112,82116) = 2⁶ × 1283¹ × 3² × 2281¹
LCM(82112,82116) = 1685677248