What is the Least Common Multiple of 82185 and 82200?

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 82185 and 82200 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 82185 and 82200, than apply into the LCM equation.

GCF(82185,82200) = 15
LCM(82185,82200) = ( 82185 × 82200) / 15
LCM(82185,82200) = 6755607000 / 15
LCM(82185,82200) = 450373800

Least Common Multiple (LCM) of 82185 and 82200 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 82185 and 82200. First we will calculate the prime factors of 82185 and 82200.

Prime Factorization of 82185

Prime Factorization of 82200

Now multiplying the highest exponent prime factors to calculate the LCM of 82185 and 82200.

LCM(82185,82200) = 3¹ × 5² × 5479¹ × 2³ × 137¹
LCM(82185,82200) = 450373800