What is the Least Common Multiple of 10000 and 10007?

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 10000 and 10007 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10000 and 10007, than apply into the LCM equation.

GCF(10000,10007) = 1
LCM(10000,10007) = ( 10000 × 10007) / 1
LCM(10000,10007) = 100070000 / 1
LCM(10000,10007) = 100070000

Least Common Multiple (LCM) of 10000 and 10007 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10000 and 10007. First we will calculate the prime factors of 10000 and 10007.

Prime Factorization of 10000

Prime Factorization of 10007

Now multiplying the highest exponent prime factors to calculate the LCM of 10000 and 10007.

LCM(10000,10007) = 2⁴ × 5⁴ × 10007¹
LCM(10000,10007) = 100070000