What is the Least Common Multiple of 6900 and 6909?

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 6900 and 6909 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6900 and 6909, than apply into the LCM equation.

GCF(6900,6909) = 3
LCM(6900,6909) = ( 6900 × 6909) / 3
LCM(6900,6909) = 47672100 / 3
LCM(6900,6909) = 15890700

Least Common Multiple (LCM) of 6900 and 6909 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 6900 and 6909. First we will calculate the prime factors of 6900 and 6909.

Prime Factorization of 6900

Prime Factorization of 6909

Now multiplying the highest exponent prime factors to calculate the LCM of 6900 and 6909.

LCM(6900,6909) = 2² × 3¹ × 5² × 23¹ × 7² × 47¹
LCM(6900,6909) = 15890700