What is the Least Common Multiple of 30000 and 30009?

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 30000 and 30009 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30000 and 30009, than apply into the LCM equation.

GCF(30000,30009) = 3
LCM(30000,30009) = ( 30000 × 30009) / 3
LCM(30000,30009) = 900270000 / 3
LCM(30000,30009) = 300090000

Least Common Multiple (LCM) of 30000 and 30009 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30000 and 30009. First we will calculate the prime factors of 30000 and 30009.

Prime Factorization of 30000

Prime Factorization of 30009

Now multiplying the highest exponent prime factors to calculate the LCM of 30000 and 30009.

LCM(30000,30009) = 2⁴ × 3¹ × 5⁴ × 7¹ × 1429¹
LCM(30000,30009) = 300090000