What is the Least Common Multiple of 20000 and 20009?

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 20000 and 20009 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 20000 and 20009, than apply into the LCM equation.

GCF(20000,20009) = 1
LCM(20000,20009) = ( 20000 × 20009) / 1
LCM(20000,20009) = 400180000 / 1
LCM(20000,20009) = 400180000

Least Common Multiple (LCM) of 20000 and 20009 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 20000 and 20009. First we will calculate the prime factors of 20000 and 20009.

Prime Factorization of 20000

Prime Factorization of 20009

Now multiplying the highest exponent prime factors to calculate the LCM of 20000 and 20009.

LCM(20000,20009) = 2⁵ × 5⁴ × 11¹ × 17¹ × 107¹
LCM(20000,20009) = 400180000