What is the Least Common Multiple of 900 and 909?

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 900 and 909 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 900 and 909, than apply into the LCM equation.

GCF(900,909) = 9
LCM(900,909) = ( 900 × 909) / 9
LCM(900,909) = 818100 / 9
LCM(900,909) = 90900

Least Common Multiple (LCM) of 900 and 909 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 900 and 909. First we will calculate the prime factors of 900 and 909.

Prime Factorization of 900

Prime Factorization of 909

Now multiplying the highest exponent prime factors to calculate the LCM of 900 and 909.

LCM(900,909) = 2² × 3² × 5² × 101¹
LCM(900,909) = 90900