What is the Least Common Multiple of 10200 and 10209?

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 10200 and 10209 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10200 and 10209, than apply into the LCM equation.

GCF(10200,10209) = 3
LCM(10200,10209) = ( 10200 × 10209) / 3
LCM(10200,10209) = 104131800 / 3
LCM(10200,10209) = 34710600

Least Common Multiple (LCM) of 10200 and 10209 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10200 and 10209. First we will calculate the prime factors of 10200 and 10209.

Prime Factorization of 10200

Prime Factorization of 10209

Now multiplying the highest exponent prime factors to calculate the LCM of 10200 and 10209.

LCM(10200,10209) = 2³ × 3¹ × 5² × 17¹ × 41¹ × 83¹
LCM(10200,10209) = 34710600