What is the Least Common Multiple of 9000 and 9009?

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 9000 and 9009 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9000 and 9009, than apply into the LCM equation.

GCF(9000,9009) = 9
LCM(9000,9009) = ( 9000 × 9009) / 9
LCM(9000,9009) = 81081000 / 9
LCM(9000,9009) = 9009000

Least Common Multiple (LCM) of 9000 and 9009 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9000 and 9009. First we will calculate the prime factors of 9000 and 9009.

Prime Factorization of 9000

Prime Factorization of 9009

Now multiplying the highest exponent prime factors to calculate the LCM of 9000 and 9009.

LCM(9000,9009) = 2³ × 3² × 5³ × 7¹ × 11¹ × 13¹
LCM(9000,9009) = 9009000