What is the Least Common Multiple of 10005 and 10020?

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 10020 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 10020, than apply into the LCM equation.

GCF(10005,10020) = 15
LCM(10005,10020) = ( 10005 × 10020) / 15
LCM(10005,10020) = 100250100 / 15
LCM(10005,10020) = 6683340

Least Common Multiple (LCM) of 10005 and 10020 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10005 and 10020. First we will calculate the prime factors of 10005 and 10020.

Prime Factorization of 10005

Prime Factorization of 10020

Now multiplying the highest exponent prime factors to calculate the LCM of 10005 and 10020.

LCM(10005,10020) = 3¹ × 5¹ × 23¹ × 29¹ × 2² × 167¹
LCM(10005,10020) = 6683340