What is the Least Common Multiple of 85200 and 85210?

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 85210 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 85210, than apply into the LCM equation.

GCF(85200,85210) = 10
LCM(85200,85210) = ( 85200 × 85210) / 10
LCM(85200,85210) = 7259892000 / 10
LCM(85200,85210) = 725989200

Least Common Multiple (LCM) of 85200 and 85210 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 85200 and 85210. First we will calculate the prime factors of 85200 and 85210.

Prime Factorization of 85200

Prime Factorization of 85210

Now multiplying the highest exponent prime factors to calculate the LCM of 85200 and 85210.

LCM(85200,85210) = 2⁴ × 3¹ × 5² × 71¹ × 8521¹
LCM(85200,85210) = 725989200