What is the Least Common Multiple of 2024 and 2040?

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 2024 and 2040 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2024 and 2040, than apply into the LCM equation.

GCF(2024,2040) = 8
LCM(2024,2040) = ( 2024 × 2040) / 8
LCM(2024,2040) = 4128960 / 8
LCM(2024,2040) = 516120

Least Common Multiple (LCM) of 2024 and 2040 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2024 and 2040. First we will calculate the prime factors of 2024 and 2040.

Prime Factorization of 2024

Prime Factorization of 2040

Now multiplying the highest exponent prime factors to calculate the LCM of 2024 and 2040.

LCM(2024,2040) = 2³ × 11¹ × 23¹ × 3¹ × 5¹ × 17¹
LCM(2024,2040) = 516120