What is the Least Common Multiple of 10005 and 10015?

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 10005 and 10015 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10005 and 10015, than apply into the LCM equation.

GCF(10005,10015) = 5
LCM(10005,10015) = ( 10005 × 10015) / 5
LCM(10005,10015) = 100200075 / 5
LCM(10005,10015) = 20040015

Least Common Multiple (LCM) of 10005 and 10015 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10005 and 10015. First we will calculate the prime factors of 10005 and 10015.

Prime Factorization of 10005

Prime Factorization of 10015

Now multiplying the highest exponent prime factors to calculate the LCM of 10005 and 10015.

LCM(10005,10015) = 3¹ × 5¹ × 23¹ × 29¹ × 2003¹
LCM(10005,10015) = 20040015