What is the Least Common Multiple of 7200 and 7209?

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 7200 and 7209 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7200 and 7209, than apply into the LCM equation.

GCF(7200,7209) = 9
LCM(7200,7209) = ( 7200 × 7209) / 9
LCM(7200,7209) = 51904800 / 9
LCM(7200,7209) = 5767200

Least Common Multiple (LCM) of 7200 and 7209 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7200 and 7209. First we will calculate the prime factors of 7200 and 7209.

Prime Factorization of 7200

Prime Factorization of 7209

Now multiplying the highest exponent prime factors to calculate the LCM of 7200 and 7209.

LCM(7200,7209) = 2⁵ × 3⁴ × 5² × 89¹
LCM(7200,7209) = 5767200