What is the Least Common Multiple of 300 and 309?

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 300 and 309 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 300 and 309, than apply into the LCM equation.

GCF(300,309) = 3
LCM(300,309) = ( 300 × 309) / 3
LCM(300,309) = 92700 / 3
LCM(300,309) = 30900

Least Common Multiple (LCM) of 300 and 309 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 300 and 309. First we will calculate the prime factors of 300 and 309.

Prime Factorization of 300

Prime Factorization of 309

Now multiplying the highest exponent prime factors to calculate the LCM of 300 and 309.

LCM(300,309) = 2² × 3¹ × 5² × 103¹
LCM(300,309) = 30900