What is the Least Common Multiple of 10008 and 10013?

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 10008 and 10013 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10008 and 10013, than apply into the LCM equation.

GCF(10008,10013) = 1
LCM(10008,10013) = ( 10008 × 10013) / 1
LCM(10008,10013) = 100210104 / 1
LCM(10008,10013) = 100210104

Least Common Multiple (LCM) of 10008 and 10013 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10008 and 10013. First we will calculate the prime factors of 10008 and 10013.

Prime Factorization of 10008

Prime Factorization of 10013

Now multiplying the highest exponent prime factors to calculate the LCM of 10008 and 10013.

LCM(10008,10013) = 2³ × 3² × 139¹ × 17¹ × 19¹ × 31¹
LCM(10008,10013) = 100210104