What is the Least Common Multiple of 82080 and 82100?

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 82080 and 82100 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 82080 and 82100, than apply into the LCM equation.

GCF(82080,82100) = 20
LCM(82080,82100) = ( 82080 × 82100) / 20
LCM(82080,82100) = 6738768000 / 20
LCM(82080,82100) = 336938400

Least Common Multiple (LCM) of 82080 and 82100 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 82080 and 82100. First we will calculate the prime factors of 82080 and 82100.

Prime Factorization of 82080

Prime Factorization of 82100

Now multiplying the highest exponent prime factors to calculate the LCM of 82080 and 82100.

LCM(82080,82100) = 2⁵ × 3³ × 5² × 19¹ × 821¹
LCM(82080,82100) = 336938400