What is the Least Common Multiple of 69000 and 69009?

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 69000 and 69009 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 69000 and 69009, than apply into the LCM equation.

GCF(69000,69009) = 3
LCM(69000,69009) = ( 69000 × 69009) / 3
LCM(69000,69009) = 4761621000 / 3
LCM(69000,69009) = 1587207000

Least Common Multiple (LCM) of 69000 and 69009 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 69000 and 69009. First we will calculate the prime factors of 69000 and 69009.

Prime Factorization of 69000

Prime Factorization of 69009

Now multiplying the highest exponent prime factors to calculate the LCM of 69000 and 69009.

LCM(69000,69009) = 2³ × 3¹ × 5³ × 23¹ × 23003¹
LCM(69000,69009) = 1587207000