What is the Least Common Multiple of 69288 and 69300?

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 69288 and 69300 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 69288 and 69300, than apply into the LCM equation.

GCF(69288,69300) = 12
LCM(69288,69300) = ( 69288 × 69300) / 12
LCM(69288,69300) = 4801658400 / 12
LCM(69288,69300) = 400138200

Least Common Multiple (LCM) of 69288 and 69300 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 69288 and 69300. First we will calculate the prime factors of 69288 and 69300.

Prime Factorization of 69288

Prime Factorization of 69300

Now multiplying the highest exponent prime factors to calculate the LCM of 69288 and 69300.

LCM(69288,69300) = 2³ × 3² × 2887¹ × 5² × 7¹ × 11¹
LCM(69288,69300) = 400138200