What is the Least Common Multiple of 10004 and 10016?

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 10004 and 10016 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10004 and 10016, than apply into the LCM equation.

GCF(10004,10016) = 4
LCM(10004,10016) = ( 10004 × 10016) / 4
LCM(10004,10016) = 100200064 / 4
LCM(10004,10016) = 25050016

Least Common Multiple (LCM) of 10004 and 10016 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10004 and 10016. First we will calculate the prime factors of 10004 and 10016.

Prime Factorization of 10004

Prime Factorization of 10016

Now multiplying the highest exponent prime factors to calculate the LCM of 10004 and 10016.

LCM(10004,10016) = 2⁵ × 41¹ × 61¹ × 313¹
LCM(10004,10016) = 25050016