What is the Least Common Multiple of 2005 and 2024?

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 2005 and 2024 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2005 and 2024, than apply into the LCM equation.

GCF(2005,2024) = 1
LCM(2005,2024) = ( 2005 × 2024) / 1
LCM(2005,2024) = 4058120 / 1
LCM(2005,2024) = 4058120

Least Common Multiple (LCM) of 2005 and 2024 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2005 and 2024. First we will calculate the prime factors of 2005 and 2024.

Prime Factorization of 2005

Prime Factorization of 2024

Now multiplying the highest exponent prime factors to calculate the LCM of 2005 and 2024.

LCM(2005,2024) = 5¹ × 401¹ × 2³ × 11¹ × 23¹
LCM(2005,2024) = 4058120