What is the Least Common Multiple of 39000 and 39009?

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 39000 and 39009 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39000 and 39009, than apply into the LCM equation.

GCF(39000,39009) = 3
LCM(39000,39009) = ( 39000 × 39009) / 3
LCM(39000,39009) = 1521351000 / 3
LCM(39000,39009) = 507117000

Least Common Multiple (LCM) of 39000 and 39009 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39000 and 39009. First we will calculate the prime factors of 39000 and 39009.

Prime Factorization of 39000

Prime Factorization of 39009

Now multiplying the highest exponent prime factors to calculate the LCM of 39000 and 39009.

LCM(39000,39009) = 2³ × 3¹ × 5³ × 13¹ × 13003¹
LCM(39000,39009) = 507117000