What is the Least Common Multiple of 85200 and 85209?

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 85200 and 85209 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 85200 and 85209, than apply into the LCM equation.

GCF(85200,85209) = 3
LCM(85200,85209) = ( 85200 × 85209) / 3
LCM(85200,85209) = 7259806800 / 3
LCM(85200,85209) = 2419935600

Least Common Multiple (LCM) of 85200 and 85209 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 85200 and 85209. First we will calculate the prime factors of 85200 and 85209.

Prime Factorization of 85200

Prime Factorization of 85209

Now multiplying the highest exponent prime factors to calculate the LCM of 85200 and 85209.

LCM(85200,85209) = 2⁴ × 3¹ × 5² × 71¹ × 28403¹
LCM(85200,85209) = 2419935600