What is the Least Common Multiple of 33000 and 33009?

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 33000 and 33009 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 33000 and 33009, than apply into the LCM equation.

GCF(33000,33009) = 3
LCM(33000,33009) = ( 33000 × 33009) / 3
LCM(33000,33009) = 1089297000 / 3
LCM(33000,33009) = 363099000

Least Common Multiple (LCM) of 33000 and 33009 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 33000 and 33009. First we will calculate the prime factors of 33000 and 33009.

Prime Factorization of 33000

Prime Factorization of 33009

Now multiplying the highest exponent prime factors to calculate the LCM of 33000 and 33009.

LCM(33000,33009) = 2³ × 3¹ × 5³ × 11¹ × 11003¹
LCM(33000,33009) = 363099000