What is the Least Common Multiple of 10006 and 10024?

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 10006 and 10024 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10006 and 10024, than apply into the LCM equation.

GCF(10006,10024) = 2
LCM(10006,10024) = ( 10006 × 10024) / 2
LCM(10006,10024) = 100300144 / 2
LCM(10006,10024) = 50150072

Least Common Multiple (LCM) of 10006 and 10024 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10006 and 10024. First we will calculate the prime factors of 10006 and 10024.

Prime Factorization of 10006

Prime Factorization of 10024

Now multiplying the highest exponent prime factors to calculate the LCM of 10006 and 10024.

LCM(10006,10024) = 2³ × 5003¹ × 7¹ × 179¹
LCM(10006,10024) = 50150072